Optionalities in the Electricity Market The Case ofCross-Border Capacity Rights

ETH Practitioner Seminar in Financial and Insurance Mathematics

Markus Regez

Axpo Trading AG

November 15 2016

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Peculiarities of the Energy market IDepending on the ability to store the commodity and the correspondingcosts time series of energy prices may show the following

I Seasonality of prices (hoursweekdaysmonths) depending onthe exact delivery period

I Connection between forward price f Tt observed at time t with

delivery at T and spot price St = f tt different to equity markets

because cash-and-carry transactions are costly (eg storagecosts) or not possible Hence f T

t er(Tminust)St does not hold ingeneral

I prices can get negativeI Spikes (rapid upward movements followed by downward

movements of the same order of magnitude) in spot prices

I Jumps in forward prices (up or down)

I Mean reversion of spot prices

I Samuleson (1965) effect (historicalimplied volatility isdecreasing with time to maturity)

Peculiarities of the Energy market II

I Cointegration of Spot prices across markets of the samecommodity across commodities

I Correlations across commodities increase with maturity (egcorrelation between gas and power for the forward productsdelivering next month is lower than the correlation between gasand power for the forward products delivering in 2020)

Example of Markets I

Coal API2I No or only weak seasonal behaviour no spikesI Delivery location Rotterdam (NLD)I illiquidI Financial swaps traded OTC and Futuresoptions on ICE (London)

Oil Brent crude oil

I No or only weak seasonal behaviour no spikesI From the North seaI Futuresoptions traded on ICE (London)

Electricity German BaseloadI not storableI Hourly spot prices exhibit mean reversion seasonality and spikesI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at EEX (European

Energy Exchange in Leipzig)

Example of Markets II

Natural Gas TTF (Dutch Gas)I partly storableI Spot prices exhibit mean reversion seasonality and spikes but

less than electricityI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at ICEEEX

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Peculiarities of the Energy market IDepending on the ability to store the commodity and the correspondingcosts time series of energy prices may show the following

I Seasonality of prices (hoursweekdaysmonths) depending onthe exact delivery period

I Connection between forward price f Tt observed at time t with

delivery at T and spot price St = f tt different to equity markets

because cash-and-carry transactions are costly (eg storagecosts) or not possible Hence f T

t er(Tminust)St does not hold ingeneral

I prices can get negativeI Spikes (rapid upward movements followed by downward

movements of the same order of magnitude) in spot prices

I Jumps in forward prices (up or down)

I Mean reversion of spot prices

I Samuleson (1965) effect (historicalimplied volatility isdecreasing with time to maturity)

Peculiarities of the Energy market II

I Cointegration of Spot prices across markets of the samecommodity across commodities

I Correlations across commodities increase with maturity (egcorrelation between gas and power for the forward productsdelivering next month is lower than the correlation between gasand power for the forward products delivering in 2020)

Example of Markets I

Coal API2I No or only weak seasonal behaviour no spikesI Delivery location Rotterdam (NLD)I illiquidI Financial swaps traded OTC and Futuresoptions on ICE (London)

Oil Brent crude oil

I No or only weak seasonal behaviour no spikesI From the North seaI Futuresoptions traded on ICE (London)

Electricity German BaseloadI not storableI Hourly spot prices exhibit mean reversion seasonality and spikesI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at EEX (European

Energy Exchange in Leipzig)

Example of Markets II

Natural Gas TTF (Dutch Gas)I partly storableI Spot prices exhibit mean reversion seasonality and spikes but

less than electricityI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at ICEEEX

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Peculiarities of the Energy market IDepending on the ability to store the commodity and the correspondingcosts time series of energy prices may show the following

I Seasonality of prices (hoursweekdaysmonths) depending onthe exact delivery period

I Connection between forward price f Tt observed at time t with

delivery at T and spot price St = f tt different to equity markets

because cash-and-carry transactions are costly (eg storagecosts) or not possible Hence f T

t er(Tminust)St does not hold ingeneral

I prices can get negativeI Spikes (rapid upward movements followed by downward

movements of the same order of magnitude) in spot prices

I Jumps in forward prices (up or down)

I Mean reversion of spot prices

I Samuleson (1965) effect (historicalimplied volatility isdecreasing with time to maturity)

Peculiarities of the Energy market II

I Cointegration of Spot prices across markets of the samecommodity across commodities

I Correlations across commodities increase with maturity (egcorrelation between gas and power for the forward productsdelivering next month is lower than the correlation between gasand power for the forward products delivering in 2020)

Example of Markets I

Coal API2I No or only weak seasonal behaviour no spikesI Delivery location Rotterdam (NLD)I illiquidI Financial swaps traded OTC and Futuresoptions on ICE (London)

Oil Brent crude oil

I No or only weak seasonal behaviour no spikesI From the North seaI Futuresoptions traded on ICE (London)

Electricity German BaseloadI not storableI Hourly spot prices exhibit mean reversion seasonality and spikesI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at EEX (European

Energy Exchange in Leipzig)

Example of Markets II

Natural Gas TTF (Dutch Gas)I partly storableI Spot prices exhibit mean reversion seasonality and spikes but

less than electricityI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at ICEEEX

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Peculiarities of the Energy market IDepending on the ability to store the commodity and the correspondingcosts time series of energy prices may show the following

I Seasonality of prices (hoursweekdaysmonths) depending onthe exact delivery period

I Connection between forward price f Tt observed at time t with

delivery at T and spot price St = f tt different to equity markets

because cash-and-carry transactions are costly (eg storagecosts) or not possible Hence f T

t er(Tminust)St does not hold ingeneral

I prices can get negativeI Spikes (rapid upward movements followed by downward

movements of the same order of magnitude) in spot prices

I Jumps in forward prices (up or down)

I Mean reversion of spot prices

I Samuleson (1965) effect (historicalimplied volatility isdecreasing with time to maturity)

Peculiarities of the Energy market II

I Cointegration of Spot prices across markets of the samecommodity across commodities

I Correlations across commodities increase with maturity (egcorrelation between gas and power for the forward productsdelivering next month is lower than the correlation between gasand power for the forward products delivering in 2020)

Example of Markets I

Coal API2I No or only weak seasonal behaviour no spikesI Delivery location Rotterdam (NLD)I illiquidI Financial swaps traded OTC and Futuresoptions on ICE (London)

Oil Brent crude oil

I No or only weak seasonal behaviour no spikesI From the North seaI Futuresoptions traded on ICE (London)

Electricity German BaseloadI not storableI Hourly spot prices exhibit mean reversion seasonality and spikesI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at EEX (European

Energy Exchange in Leipzig)

Example of Markets II

Natural Gas TTF (Dutch Gas)I partly storableI Spot prices exhibit mean reversion seasonality and spikes but

less than electricityI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at ICEEEX

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Peculiarities of the Energy market II

I Cointegration of Spot prices across markets of the samecommodity across commodities

I Correlations across commodities increase with maturity (egcorrelation between gas and power for the forward productsdelivering next month is lower than the correlation between gasand power for the forward products delivering in 2020)

Example of Markets I

Coal API2I No or only weak seasonal behaviour no spikesI Delivery location Rotterdam (NLD)I illiquidI Financial swaps traded OTC and Futuresoptions on ICE (London)

Oil Brent crude oil

I No or only weak seasonal behaviour no spikesI From the North seaI Futuresoptions traded on ICE (London)

Electricity German BaseloadI not storableI Hourly spot prices exhibit mean reversion seasonality and spikesI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at EEX (European

Energy Exchange in Leipzig)

Example of Markets II

Natural Gas TTF (Dutch Gas)I partly storableI Spot prices exhibit mean reversion seasonality and spikes but

less than electricityI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at ICEEEX

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Example of Markets I

Coal API2I No or only weak seasonal behaviour no spikesI Delivery location Rotterdam (NLD)I illiquidI Financial swaps traded OTC and Futuresoptions on ICE (London)

Oil Brent crude oil

I No or only weak seasonal behaviour no spikesI From the North seaI Futuresoptions traded on ICE (London)

Electricity German BaseloadI not storableI Hourly spot prices exhibit mean reversion seasonality and spikesI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at EEX (European

Energy Exchange in Leipzig)

Example of Markets II

Natural Gas TTF (Dutch Gas)I partly storableI Spot prices exhibit mean reversion seasonality and spikes but

less than electricityI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at ICEEEX

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Example of Markets II

Natural Gas TTF (Dutch Gas)I partly storableI Spot prices exhibit mean reversion seasonality and spikes but

less than electricityI Delivery happens during a time period rather than at a time pointI Forwardsoptions traded OTC and Futures at ICEEEX

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Overview electricity market

Generation Companies

System Operators

Market Operators

Retailers

Large Consumers

OTC

OTC

Buy from producers sell to end-usersgenerates electricity

provides balancing service

auction transmision rights

ensure reliability and security

operate the market

organize exchanges

Figure Illustration of the main players in the Electricity market Based onCornlusse (2014)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Introduction I

I Electricity in the wholesale market is delivered over a time periodat a specified place (called rsquobalancing grouprsquo) with a specifiedpower expressed in Megawatt (MW) This makes it different tothe stock or the interest market for instance where stocks andpayments are exchanged at certain particular time points and notduring a period Finally the price is quoted in terms of MWh egif we exchange 4 MW during 5 hours we have exchanged 20MWh of energy

I Balancing groups are grouped together to rsquogrid zonesrsquo for whichan entity called TSO (Transmission system operator) needs tomake sure that electricity production is at any time equal toelectricity consumption (according to Kirchhoffrsquos circuit laws) Inorder to ensure this the TSO needs to have the possibility toincreasedecrease consumptionproduction (and the opposite) atany time to ensure a balanced grid

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Introduction III Grid zones are connected via Transmission lines with certain

capacities

I We can mainly distinguish two markets (leaving aside the veryshort term markets) Spot markets and forward marketsTypically on the spot market hourly blocks of power delivered onthe following day are auctioned In the forward market electricitydelivered during blocks of days weekends weeks monthsquarters or years are traded

I The spot market is organized for auctions for every hour in everygridzone Every participant can enter constrained bids or offers(like participant A is willing to sell tomorrow in the hour from0600 to 0700 in Germany 20 MW for a price above 30EURMWh 15 MW for a price between 20 and 30 EURMWh and10 MW below a price of 20 EURMWh) The auction organizer(an exchange) will aggregate the Bids and Offers and calculatethe equilibrium price where demand meets supply

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Introduction III

I The forward market is organized OTC (over the counter) (whereusually physically delivered forwards or financially settled swapsare traded) and at exchanges (where usually financially settledfutures are traded)

I Absence of arbitrage requires that at time t the forward priceFT1T2

t for a product delivering in the interval [T1T2] withT2 gt T1 gt t is equal to expectation of the average spot priceduring that period under the pricing measure Q

FT1T2t = EQ

1T2 minusT1

T2intT1

Sudu |Ft

where we denote by St the (not observable) instantaneous priceof electricity delivered in time t

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Hourly spot auction illustration

Figure Electricity Demand and Supply Curves in France 1600-1700 onNovember 3 2016 Source wwwepexspotcom

Historical hourly Spot prices of French electricity firstimpression

0

1000

2000

3000

2006 2008 2010 2012 2014 2016Date

EU

RM

Wh

Figure hourly Spot prices for France Datasource EpexSpot

Historical Spot prices of France A better impression

0

200

400

600

2006 2008 2010 2012 2014 2016Date

EU

RM

Wh

Figure Daily and weekly averaged Spot prices for France DatasourceEpexSpot

Historical Spot prices of France within-year seasonality

50

100

150

0 10 20 30 40 50week

EU

RM

Wh

year

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

2016

Figure Weekly averaged spot prices for France for different yearsDatasource EpexSpot

Historical Spot prices of France weekdayweekendseasonality

25

50

75

100

125

Jan 2016 Apr 2016 Jul 2016 Okt 2016Date

EU

RM

Wh

Figure Daily averaged spot prices for France Datasource EpexSpot

Historical Spot prices of France within-week seasonality

Mon Tue Wed Thu Fri Sat Sun0

50

100

150

0 24 48 72 96 120 144hour in week

EU

RM

Wh weekName

2016minus43

2016minus44

Figure Hourly spot prices of France for two Weeks Datasource EpexSpot

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Structural models I

I Structural or fundamental models model the economic variableswhich affect the formation of the electricity price

I Usually these variables will either have an impact on the supplyor the demand of electricity

I On the production side usually the merit-order-curve ismodelled which rsquoranksrsquo different production technologiesaccording to their marginal short run costs Potential variables tomodel are fuel prices which affect the marginal costs of gas orcoal-fired-power plants or unexpected outages of power plantsor subsidies for green energy which will foster long term buildingof wind or solar power plants

I On the demand side short term factors like wind strengthtemperatures or economic output growth are variables whichcan be considered

I By simulating these variables market clearing prices arecalculated which finally will lead to a series of spot prices

Structural models III These models are often not tractable such that they can hardly

be calibrated to market dataI They are often used for scenario analysis to estimate the impact

of a change in an external variablesI Examples of these models are from Barlow (2002) or Carmona

et al (2013)

Figure Merit Order Source EIA

Structural models I

I Structural or fundamental models model the economic variableswhich affect the formation of the electricity price

I Usually these variables will either have an impact on the supplyor the demand of electricity

I On the production side usually the merit-order-curve ismodelled which rsquoranksrsquo different production technologiesaccording to their marginal short run costs Potential variables tomodel are fuel prices which affect the marginal costs of gas orcoal-fired-power plants or unexpected outages of power plantsor subsidies for green energy which will foster long term buildingof wind or solar power plants

I On the demand side short term factors like wind strengthtemperatures or economic output growth are variables whichcan be considered

I By simulating these variables market clearing prices arecalculated which finally will lead to a series of spot prices

Structural models III These models are often not tractable such that they can hardly

be calibrated to market dataI They are often used for scenario analysis to estimate the impact

of a change in an external variablesI Examples of these models are from Barlow (2002) or Carmona

et al (2013)

Figure Merit Order Source EIA

Structural models III These models are often not tractable such that they can hardly

be calibrated to market dataI They are often used for scenario analysis to estimate the impact

of a change in an external variablesI Examples of these models are from Barlow (2002) or Carmona

et al (2013)

Figure Merit Order Source EIA

Example of France forwards I

I On the end of September 2016 EDF (the French utility)communicated that some of their nuclear power plants have to gointo extended maintenance 21 of the 58 plants in France areoffline Therefore it was expected that supply will be limited

I On the end of October 2016 meteorologists forecasted lowtemperatures for the week beginning on November 07 2016Since heating with electricity is common in France a highdemand in that week was expected

Example of France forwards II

50

100

150

200

250

Aug Sep Okt Novtime

pric

e

productName

month2016minus11minus01

week2016minus10minus31

week2016minus11minus07

week2016minus11minus14

week2016minus11minus21

week2016minus11minus28

Figure Weekly and Monthly forward prices for France delivering in November2016 Datasource EEX

One simple model Barlow (2002) I

The model of Barlow (2002) is a very simple model which directlymodels the electricity demand Xt by a standard Ornstein-Uhlenbeckprocess (demand is mean reverting because the weather is meanreverting) and not dependent on any price because demand isinelastic

dXt =minusλ (Xt minus x)dt+σdWt

Marginal short run costs (supply curve) are given by the functionfα (Xt)

fα (Xt) =

(1+αXt)

1α if α = 0eXt if α = 0

The level of α sets the elasticity of electricity supplyThe final spot price St is given by the market clearing price wheredemand meets supply However a maximum threshold is set (which

One simple model Barlow (2002) II

can be justified since spot markets usually really have an upperthreshold price)

S (t) =

fα (Xt) if 1+αXt gt ε0

ε1α0 if 1+αXt 6 ε0

Spot factor models ISpot factor models explain the evolution of spot prices by severalfactors Meyer-Brandis amp Tankov (2008) for example use twomean-reverting factors

St = eΛt middot(Y1

t +Y2t)

dY1t =minus 1

λ1Y1

t dt+σdWt

dY2t =minus 1

λ2Y2

t dt+dLt

Lt =Nt

sumi=1

Di

where Lt is a compound Poisson process where the jump sizes Di

are Pareto distributed λ1λ2 gt 0 and Λt represents a deterministicseasonalityNote that authors (for example Koekebakker amp Ollmar (2005)) whoperformed a PCA analysis on electricity price data concluded that

Spot factor models II

many factors (gt 3) are required to explain a reasonable fraction ofthe variation in electricity prices This is more than in other markets

Plot of Forwardprices

20

30

40

50

60

2012 2013 2014 2015 2016Date

pric

e E

UR

MW

h

colour

M1

M2

M3

Q1

Q2

Q3

Y1

Y2

Y3

Figure History of Futures prices of French Baseload Power DataSourceEEX

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

Example of France forwards II

50

100

150

200

250

Aug Sep Okt Novtime

pric

e

productName

month2016minus11minus01

week2016minus10minus31

week2016minus11minus07

week2016minus11minus14

week2016minus11minus21

week2016minus11minus28

Figure Weekly and Monthly forward prices for France delivering in November2016 Datasource EEX

One simple model Barlow (2002) I

The model of Barlow (2002) is a very simple model which directlymodels the electricity demand Xt by a standard Ornstein-Uhlenbeckprocess (demand is mean reverting because the weather is meanreverting) and not dependent on any price because demand isinelastic

dXt =minusλ (Xt minus x)dt+σdWt

Marginal short run costs (supply curve) are given by the functionfα (Xt)

fα (Xt) =

(1+αXt)

1α if α = 0eXt if α = 0

The level of α sets the elasticity of electricity supplyThe final spot price St is given by the market clearing price wheredemand meets supply However a maximum threshold is set (which

One simple model Barlow (2002) II

can be justified since spot markets usually really have an upperthreshold price)

S (t) =

fα (Xt) if 1+αXt gt ε0

ε1α0 if 1+αXt 6 ε0

Spot factor models ISpot factor models explain the evolution of spot prices by severalfactors Meyer-Brandis amp Tankov (2008) for example use twomean-reverting factors

St = eΛt middot(Y1

t +Y2t)

dY1t =minus 1

λ1Y1

t dt+σdWt

dY2t =minus 1

λ2Y2

t dt+dLt

Lt =Nt

sumi=1

Di

where Lt is a compound Poisson process where the jump sizes Di

are Pareto distributed λ1λ2 gt 0 and Λt represents a deterministicseasonalityNote that authors (for example Koekebakker amp Ollmar (2005)) whoperformed a PCA analysis on electricity price data concluded that

Spot factor models II

many factors (gt 3) are required to explain a reasonable fraction ofthe variation in electricity prices This is more than in other markets

Plot of Forwardprices

20

30

40

50

60

2012 2013 2014 2015 2016Date

pric

e E

UR

MW

h

colour

M1

M2

M3

Q1

Q2

Q3

Y1

Y2

Y3

Figure History of Futures prices of French Baseload Power DataSourceEEX

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

One simple model Barlow (2002) I

The model of Barlow (2002) is a very simple model which directlymodels the electricity demand Xt by a standard Ornstein-Uhlenbeckprocess (demand is mean reverting because the weather is meanreverting) and not dependent on any price because demand isinelastic

dXt =minusλ (Xt minus x)dt+σdWt

Marginal short run costs (supply curve) are given by the functionfα (Xt)

fα (Xt) =

(1+αXt)

1α if α = 0eXt if α = 0

The level of α sets the elasticity of electricity supplyThe final spot price St is given by the market clearing price wheredemand meets supply However a maximum threshold is set (which

One simple model Barlow (2002) II

can be justified since spot markets usually really have an upperthreshold price)

S (t) =

fα (Xt) if 1+αXt gt ε0

ε1α0 if 1+αXt 6 ε0

Spot factor models ISpot factor models explain the evolution of spot prices by severalfactors Meyer-Brandis amp Tankov (2008) for example use twomean-reverting factors

St = eΛt middot(Y1

t +Y2t)

dY1t =minus 1

λ1Y1

t dt+σdWt

dY2t =minus 1

λ2Y2

t dt+dLt

Lt =Nt

sumi=1

Di

where Lt is a compound Poisson process where the jump sizes Di

are Pareto distributed λ1λ2 gt 0 and Λt represents a deterministicseasonalityNote that authors (for example Koekebakker amp Ollmar (2005)) whoperformed a PCA analysis on electricity price data concluded that

Spot factor models II

many factors (gt 3) are required to explain a reasonable fraction ofthe variation in electricity prices This is more than in other markets

Plot of Forwardprices

20

30

40

50

60

2012 2013 2014 2015 2016Date

pric

e E

UR

MW

h

colour

M1

M2

M3

Q1

Q2

Q3

Y1

Y2

Y3

Figure History of Futures prices of French Baseload Power DataSourceEEX

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

One simple model Barlow (2002) II

can be justified since spot markets usually really have an upperthreshold price)

S (t) =

fα (Xt) if 1+αXt gt ε0

ε1α0 if 1+αXt 6 ε0

Spot factor models ISpot factor models explain the evolution of spot prices by severalfactors Meyer-Brandis amp Tankov (2008) for example use twomean-reverting factors

St = eΛt middot(Y1

t +Y2t)

dY1t =minus 1

λ1Y1

t dt+σdWt

dY2t =minus 1

λ2Y2

t dt+dLt

Lt =Nt

sumi=1

Di

where Lt is a compound Poisson process where the jump sizes Di

are Pareto distributed λ1λ2 gt 0 and Λt represents a deterministicseasonalityNote that authors (for example Koekebakker amp Ollmar (2005)) whoperformed a PCA analysis on electricity price data concluded that

Spot factor models II

many factors (gt 3) are required to explain a reasonable fraction ofthe variation in electricity prices This is more than in other markets

Plot of Forwardprices

20

30

40

50

60

2012 2013 2014 2015 2016Date

pric

e E

UR

MW

h

colour

M1

M2

M3

Q1

Q2

Q3

Y1

Y2

Y3

Figure History of Futures prices of French Baseload Power DataSourceEEX

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

Spot factor models ISpot factor models explain the evolution of spot prices by severalfactors Meyer-Brandis amp Tankov (2008) for example use twomean-reverting factors

St = eΛt middot(Y1

t +Y2t)

dY1t =minus 1

λ1Y1

t dt+σdWt

dY2t =minus 1

λ2Y2

t dt+dLt

Lt =Nt

sumi=1

Di

where Lt is a compound Poisson process where the jump sizes Di

are Pareto distributed λ1λ2 gt 0 and Λt represents a deterministicseasonalityNote that authors (for example Koekebakker amp Ollmar (2005)) whoperformed a PCA analysis on electricity price data concluded that

Spot factor models II

many factors (gt 3) are required to explain a reasonable fraction ofthe variation in electricity prices This is more than in other markets

Plot of Forwardprices

20

30

40

50

60

2012 2013 2014 2015 2016Date

pric

e E

UR

MW

h

colour

M1

M2

M3

Q1

Q2

Q3

Y1

Y2

Y3

Figure History of Futures prices of French Baseload Power DataSourceEEX

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

Spot factor models II

many factors (gt 3) are required to explain a reasonable fraction ofthe variation in electricity prices This is more than in other markets

Plot of Forwardprices

20

30

40

50

60

2012 2013 2014 2015 2016Date

pric

e E

UR

MW

h

colour

M1

M2

M3

Q1

Q2

Q3

Y1

Y2

Y3

Figure History of Futures prices of French Baseload Power DataSourceEEX

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

Plot of Forwardprices

20

30

40

50

60

2012 2013 2014 2015 2016Date

pric

e E

UR

MW

h

colour

M1

M2

M3

Q1

Q2

Q3

Y1

Y2

Y3

Figure History of Futures prices of French Baseload Power DataSourceEEX

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

HPFC I

Every market player has its own hourly price forward curve (HPFC)for each market which is used to price linear electricity products ofany kind delivering in any hour An HPFC is arbitrage free withrespect to products traded in the market (the weekly monthlyquarterly yearly average of the hourly prices equals the correspondingprice of the traded observable contracts) and usually makes use ofseasonality and holiday information and smoothing considerationsSee for example Benth et al (2013 chapter 7) for one method tocreate such a curveHowever note that there are infinitely many different HPFCs which areconsistent with the observable market prices- because the market isnot complete

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

HPFC II

240

260

280

300

0 100 200 300 400time

pric

e

product

DA

MONTH

PFC

QUARTER

WEEK

YEAR

Figure Sample daily forward curve and market inputs (shifted)

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

HJM-style models I

Similar as in the interest rate world models in the spirit of Heath et al(1992) are applied where forward prices are modelled directlyUsually they use the given HPFC as a starting point - in which priceinformation about seasonality etc is already contained and hence themodel will not need to take care about thisOften the models are based on

dFT1T2t

FT1T2t

=m

sumk=1

σk (tT1T2)dWkt

where FT1T2t is the forward price at time t for the electricity delivery

during period [T1T2] with T2 gt T1 gt t and m represents the number offactors considered

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

HJM-style models II

An examples of these models is Kiesel et al (2009) where monthlyfuturesforwards with delivery during monthly periods (l denotes thelength of a month) have the folllowing SDE

dFT1T1+lt

FT1T1+lt

= eminusκ(T1minust)σ1dW1t +σ2dW2

t

Futures of periods of quarterly and yearly length are approximatedusing a basket volatility approximation formula In this model thevolatility of the long end of the curve approaches σ2 while the shortend of the curve is increasingly driven by the first factorAnother model of this class is Bjerksund et al (2010) who use adifferent approximation Also other models evolved in the meantimewith more general factors (for example based on Levy processes)

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

The product I

I Transmission line capacities between neighbouring marketsare auctioned There exist day ahead month ahead and yearahead auctions for transmission of electricity of most of theneighbouring markets- see httpwwwjaoeu

I If one owns such a transmission right to transport electricity frommarket grid zone A to market grid zone B then -depending onthe specific boarder- one either

I has the right to move electricity physically across grid zones orI owns a financial product which pays in each hour h

max(SA

h minusSBh 0

) where SA

h is the spot price of hour h in market Aand SB

h is the spot price of hour h in market B

The product II

I The physical transmission would be financially equal to thefinancial product if one would be able to transact at the spotprices of the two markets at the time when the transmission righthas to be nominated to the TSO This is however not the casesince nomination of transmission rights has to be done somehours before the spot auction is taking place Additionally inorder to benefit from the price differential of the two markets onewould need to participate in the auction of which one does notknow the outcome in advance Therefore the payoff of thephysical transmission right in hour h is equal tomax

(E[SA

h minusSBh |Fhminusd

]0) where we denote by d time

differential between nomination of the boarder and thepublication of the spot prices SA

h and SBh

The product III

I In Europe the settlement is only done financially if the marketsare part of the so called market coupling mechanism In thiscase the spot prices across the neighbouring countries aredetermined at the same time while taking into account thecapacity of the x-border lines This ensures that energy only flowsfrom market A to market B if the spot price in market B is higherthan the spot price in market A which avoids inefficiencies andincreases economic welfare

I Since physical transmission has to be nominated before the spotprice is published inefficiencies might arise

I Note that the payoff indicates that the product is financially equalto a strip of hourly spread options- where each hour of thedelivery period can be executed independently

Illustration of Market Coupling I

Figure Market Coupling without Congestion (source Adamec et al (2009))

If the capacity of the transmission line is large enough the spot pricesof market A and B are equal

Illustration of Market Coupling II

Figure Market Coupling with Congestion (source Adamec et al (2009))

If the capacity of the transmission line is large enough then theimporting market has a higher price than the exporting market

Figure Flows on 8th of November 2016 from 1800-1900 Source EpexSpot

The product III

I In Europe the settlement is only done financially if the marketsare part of the so called market coupling mechanism In thiscase the spot prices across the neighbouring countries aredetermined at the same time while taking into account thecapacity of the x-border lines This ensures that energy only flowsfrom market A to market B if the spot price in market B is higherthan the spot price in market A which avoids inefficiencies andincreases economic welfare

I Since physical transmission has to be nominated before the spotprice is published inefficiencies might arise

I Note that the payoff indicates that the product is financially equalto a strip of hourly spread options- where each hour of thedelivery period can be executed independently

Illustration of Market Coupling I

Figure Market Coupling without Congestion (source Adamec et al (2009))

If the capacity of the transmission line is large enough the spot pricesof market A and B are equal

Illustration of Market Coupling II

Figure Market Coupling with Congestion (source Adamec et al (2009))

If the capacity of the transmission line is large enough then theimporting market has a higher price than the exporting market

Figure Flows on 8th of November 2016 from 1800-1900 Source EpexSpot

Illustration of Market Coupling I

Figure Market Coupling without Congestion (source Adamec et al (2009))

If the capacity of the transmission line is large enough the spot pricesof market A and B are equal

Illustration of Market Coupling II

Figure Market Coupling with Congestion (source Adamec et al (2009))

If the capacity of the transmission line is large enough then theimporting market has a higher price than the exporting market

Figure Flows on 8th of November 2016 from 1800-1900 Source EpexSpot

Illustration of Market Coupling II

Figure Market Coupling with Congestion (source Adamec et al (2009))

If the capacity of the transmission line is large enough then theimporting market has a higher price than the exporting market

Figure Flows on 8th of November 2016 from 1800-1900 Source EpexSpot

Figure Flows on 8th of November 2016 from 1800-1900 Source EpexSpot

Intrinsic Value I

Practitioners like to split up the value of flexible products productswith optionalities into an intrinsic and a extrinsic part For theintrinsic part two different definitions are common

I The value that will result if the current HPFC will realize in thespot market so ST = f T

t

I The value that can be locked in today by trading the underlyingtoday

The extrinsic part is the residual of what is left in order to get thetotal value In a standard option setting it would also be called timevalue If we denote at time t the value of a call expiring at time T by Ctthen max(St minusK0) is the intrinsic value and Ct minusmax(St minusK0) isthe extrinsic valueAre the two definitions of the intrinsic value different (neglectingtransaction costs) In a complete market setting where the price ofthe underlying is observable and traded it is equal But a yearlytransmission right is composed of 8760 independent options which

Intrinsic Value IIhave in total 2times8760 different underlying contracts They are clearlynot tradedHence if one uses the first definition then the intrinsic value is differentacross market participants (since they all have different HPFC models)and cannot be realized immediately- itrsquos prone to modelmisspecification

Table Belgium and French electricity futures settlement price on the day ofauction (2015-12-09) and resulting intrinsic value compared to actual auctionprice outcome (in EURMWh) Datasources JAO EEX and ICEEndex

BEL FRA Spread FRA to BEL BEL to FRA days

Jan 3870 3809 061 061 0 31Feb 4070 4127 -057 0 057 29Mar 3595 3708 -113 0 113 31Q2 3060 3050 01 01 0 91Q3 3035 2969 066 066 0 92Q4 3790 3835 -045 0 045 92

Full year 3431 3432 001 024 025 366Auction 096 125

Extrinsic 072 100

Intrinsic Value IIhave in total 2times8760 different underlying contracts They are clearlynot tradedHence if one uses the first definition then the intrinsic value is differentacross market participants (since they all have different HPFC models)and cannot be realized immediately- itrsquos prone to modelmisspecification

Table Belgium and French electricity futures settlement price on the day ofauction (2015-12-09) and resulting intrinsic value compared to actual auctionprice outcome (in EURMWh) Datasources JAO EEX and ICEEndex

BEL FRA Spread FRA to BEL BEL to FRA days

Jan 3870 3809 061 061 0 31Feb 4070 4127 -057 0 057 29Mar 3595 3708 -113 0 113 31Q2 3060 3050 01 01 0 91Q3 3035 2969 066 066 0 92Q4 3790 3835 -045 0 045 92

Full year 3431 3432 001 024 025 366Auction 096 125

Extrinsic 072 100

Valuation according to Wobben et al (2012) I

Wobben et al (2012) suggest three models for valuation of physicaltransmission rights First they deseasonalize the data and then fit theresidual by considering the combinations of

I modelling the spot price spreads directly vs the individualspot prices in the two markets

I using only mean-reverting diffusion processes vs includingjumps which are independent in case of the two markets

They conclude that a setting with a correlated diffusion processes forthe two prices including jumps is the most realistic case and also claimthat the prices paid at the auctions are too lowHowever as they also note themselves physical transmission rightsare lsquoin fact [] options on the expected spot prices becausenomination takes place 4 hours before day-ahead market clearingrsquoNevertheless they fit their models to realized spot prices as if theproduct would be a financial transmission right which potentially leadsto an overvaluation

Margrabe (1978) formula I

Note that a call on the spread StAT minusSBT with strike K is exactly the

same as a put on the spread StBT minusSAT with strike minusK

The simplest approach to price a spread option with a 0 strike is givenby the Margrabe (1978) formula It uses the hourly prices of theHPFCs for the two markets AB as a starting point and then assumesthat the spot prices in both markets are multivariate log normaldistributed This formula naturally follows in a diffusionHJM-framework Then at time t the price of a call option CT

t on thespread St

AT minusSBT is given by

CTt = eminusr(Tminust) (FT

At middotN (d1)minusFTBt middotN (d2)

)d1 =

log(

FTAt

FTBt

)+ 1

2 (T minus t) middot σ2 (tT)radic

T minus t middot σ (tT)d2 =

log(

FTAt

FTBt

)minus 1

2 (T minus t) middot σ 2 (tT)radic

T minus t middot σ (tT)

σ (tT) =radic

σ 2A (tT)+σ 2

B (tT)minus2σA (tT) middotσB (tT)ρAB (tT)

Margrabe (1978) formula II

where FTAt and FT

Bt are the forward price of market A and B for adelivery in time T as observed at time t σA (tT) and σB (tT) the

annualized volatility of log(

SAT

FTAt

)and log

(SBT

FTAt

)respectively and

ρAB (tT) the corresponding correlation Usually the two volatilities aredecreasing and correlation is increasing with time to maturity T minus tNote that this formula is not justified by a replication argumentbecause the market is not complete since the two underlying productscannot be tradedAnyway a multivariate lognormal distribution seems to be notjustified when one plots the hourly prices of two neighbouringmarkets against each other

Margrabe (1978) formula III

0

50

100

150

200

0 30 60 90 120hourly price in FRA in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

25

50

75

100

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in N

LD in

EU

RM

Wh

0

30

60

90

120

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in F

RA

in E

UR

MW

h

0

50

100

150

200

25 50 75 100hourly price in NLD in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

Figure hourly spot prices of the first 6000 hours of the year 2015 of FranceBelgium Netherlands and Germany plotted against each other The red lineindicates the line of equal prices on both markets DatasourceEpexSpot

Margrabe (1978) formula IV

0

1000

2000

3000

0 20 40 60BEL minus FRA

coun

t

Figure Histogram of hourly spot price spread Belgium - France of the first6000 hours in the year 2015 DatasourceEpexSpot

Regime BEL between FRA and NLD

10

20

30

40

50

60

Jan 15 Feb 01 Feb 15 Mrz 01 Mrz 15Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe beginning of 2015 DatasourceEpexSpot

Regime NLD decoupled FRA and BEL spiky

25

50

75

100

125

Sep 01 Sep 15 Okt 01 Okt 15 Nov 01Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe end 2016 DatasourceEpexSpot

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Margrabe (1978) formula I

Note that a call on the spread StAT minusSBT with strike K is exactly the

same as a put on the spread StBT minusSAT with strike minusK

The simplest approach to price a spread option with a 0 strike is givenby the Margrabe (1978) formula It uses the hourly prices of theHPFCs for the two markets AB as a starting point and then assumesthat the spot prices in both markets are multivariate log normaldistributed This formula naturally follows in a diffusionHJM-framework Then at time t the price of a call option CT

t on thespread St

AT minusSBT is given by

CTt = eminusr(Tminust) (FT

At middotN (d1)minusFTBt middotN (d2)

)d1 =

log(

FTAt

FTBt

)+ 1

2 (T minus t) middot σ2 (tT)radic

T minus t middot σ (tT)d2 =

log(

FTAt

FTBt

)minus 1

2 (T minus t) middot σ 2 (tT)radic

T minus t middot σ (tT)

σ (tT) =radic

σ 2A (tT)+σ 2

B (tT)minus2σA (tT) middotσB (tT)ρAB (tT)

Margrabe (1978) formula II

where FTAt and FT

Bt are the forward price of market A and B for adelivery in time T as observed at time t σA (tT) and σB (tT) the

annualized volatility of log(

SAT

FTAt

)and log

(SBT

FTAt

)respectively and

ρAB (tT) the corresponding correlation Usually the two volatilities aredecreasing and correlation is increasing with time to maturity T minus tNote that this formula is not justified by a replication argumentbecause the market is not complete since the two underlying productscannot be tradedAnyway a multivariate lognormal distribution seems to be notjustified when one plots the hourly prices of two neighbouringmarkets against each other

Margrabe (1978) formula III

0

50

100

150

200

0 30 60 90 120hourly price in FRA in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

25

50

75

100

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in N

LD in

EU

RM

Wh

0

30

60

90

120

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in F

RA

in E

UR

MW

h

0

50

100

150

200

25 50 75 100hourly price in NLD in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

Figure hourly spot prices of the first 6000 hours of the year 2015 of FranceBelgium Netherlands and Germany plotted against each other The red lineindicates the line of equal prices on both markets DatasourceEpexSpot

Margrabe (1978) formula IV

0

1000

2000

3000

0 20 40 60BEL minus FRA

coun

t

Figure Histogram of hourly spot price spread Belgium - France of the first6000 hours in the year 2015 DatasourceEpexSpot

Regime BEL between FRA and NLD

10

20

30

40

50

60

Jan 15 Feb 01 Feb 15 Mrz 01 Mrz 15Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe beginning of 2015 DatasourceEpexSpot

Regime NLD decoupled FRA and BEL spiky

25

50

75

100

125

Sep 01 Sep 15 Okt 01 Okt 15 Nov 01Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe end 2016 DatasourceEpexSpot

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Margrabe (1978) formula II

where FTAt and FT

Bt are the forward price of market A and B for adelivery in time T as observed at time t σA (tT) and σB (tT) the

annualized volatility of log(

SAT

FTAt

)and log

(SBT

FTAt

)respectively and

ρAB (tT) the corresponding correlation Usually the two volatilities aredecreasing and correlation is increasing with time to maturity T minus tNote that this formula is not justified by a replication argumentbecause the market is not complete since the two underlying productscannot be tradedAnyway a multivariate lognormal distribution seems to be notjustified when one plots the hourly prices of two neighbouringmarkets against each other

Margrabe (1978) formula III

0

50

100

150

200

0 30 60 90 120hourly price in FRA in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

25

50

75

100

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in N

LD in

EU

RM

Wh

0

30

60

90

120

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in F

RA

in E

UR

MW

h

0

50

100

150

200

25 50 75 100hourly price in NLD in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

Figure hourly spot prices of the first 6000 hours of the year 2015 of FranceBelgium Netherlands and Germany plotted against each other The red lineindicates the line of equal prices on both markets DatasourceEpexSpot

Margrabe (1978) formula IV

0

1000

2000

3000

0 20 40 60BEL minus FRA

coun

t

Figure Histogram of hourly spot price spread Belgium - France of the first6000 hours in the year 2015 DatasourceEpexSpot

Regime BEL between FRA and NLD

10

20

30

40

50

60

Jan 15 Feb 01 Feb 15 Mrz 01 Mrz 15Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe beginning of 2015 DatasourceEpexSpot

Regime NLD decoupled FRA and BEL spiky

25

50

75

100

125

Sep 01 Sep 15 Okt 01 Okt 15 Nov 01Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe end 2016 DatasourceEpexSpot

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Margrabe (1978) formula III

0

50

100

150

200

0 30 60 90 120hourly price in FRA in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

25

50

75

100

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in N

LD in

EU

RM

Wh

0

30

60

90

120

minus50 0 50 100hourly price in DEU in EURMWh

hour

ly p

rice

in F

RA

in E

UR

MW

h

0

50

100

150

200

25 50 75 100hourly price in NLD in EURMWh

hour

ly p

rice

in B

EL

in E

UR

MW

h

Figure hourly spot prices of the first 6000 hours of the year 2015 of FranceBelgium Netherlands and Germany plotted against each other The red lineindicates the line of equal prices on both markets DatasourceEpexSpot

Margrabe (1978) formula IV

0

1000

2000

3000

0 20 40 60BEL minus FRA

coun

t

Figure Histogram of hourly spot price spread Belgium - France of the first6000 hours in the year 2015 DatasourceEpexSpot

Regime BEL between FRA and NLD

10

20

30

40

50

60

Jan 15 Feb 01 Feb 15 Mrz 01 Mrz 15Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe beginning of 2015 DatasourceEpexSpot

Regime NLD decoupled FRA and BEL spiky

25

50

75

100

125

Sep 01 Sep 15 Okt 01 Okt 15 Nov 01Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe end 2016 DatasourceEpexSpot

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Margrabe (1978) formula IV

0

1000

2000

3000

0 20 40 60BEL minus FRA

coun

t

Figure Histogram of hourly spot price spread Belgium - France of the first6000 hours in the year 2015 DatasourceEpexSpot

Regime BEL between FRA and NLD

10

20

30

40

50

60

Jan 15 Feb 01 Feb 15 Mrz 01 Mrz 15Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe beginning of 2015 DatasourceEpexSpot

Regime NLD decoupled FRA and BEL spiky

25

50

75

100

125

Sep 01 Sep 15 Okt 01 Okt 15 Nov 01Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe end 2016 DatasourceEpexSpot

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Regime BEL between FRA and NLD

10

20

30

40

50

60

Jan 15 Feb 01 Feb 15 Mrz 01 Mrz 15Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe beginning of 2015 DatasourceEpexSpot

Regime NLD decoupled FRA and BEL spiky

25

50

75

100

125

Sep 01 Sep 15 Okt 01 Okt 15 Nov 01Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe end 2016 DatasourceEpexSpot

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Regime NLD decoupled FRA and BEL spiky

25

50

75

100

125

Sep 01 Sep 15 Okt 01 Okt 15 Nov 01Date

EU

RM

Wh colour

BEL

FRA

NLD

Figure Daily averaged spot prices for France Belgium and Netherlands onthe end 2016 DatasourceEpexSpot

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Structural models

I Mahringer et al (2015) suggest a fundamentalstructural modelfor the spot prices in the two markets by randomizing fuel costsand the demand in the two markets They then present a closedform solution for the valuation of transmission right However nocalibration to actual data is performed

I Kiesel amp Kustermann (2015) extend the fundamental model ofCarmona et al (2013) to two markets with market couplingHowever they focus on studying the impact of market coupling onfutures prices but do not use their model to value transmissioncapacity rights

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Possibilities for further research

The literature on this topic is relatively new and there is no standardmodel yet applied A reasonable model should have

I is in line with market traded forward pricesI is able to reproduce the histogram of spreads of spot prices as

observed

I takes into account that there can be regime switches as in theBelgium market

I can be calibrated to and with historical market data

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Other products with optionalitiesIn the energy market a lot of real options are implicitly traded eitherwhen investing in an asset or in a financial products like so called VPP(virtual power plants) The problem that has to be solved for most ofthese products is path dependent and therefore the industry standardvaluation tool is the Longstaff amp Schwartz (2001) approach alsoknown as Least Square Monte Carlo or American Monte CarloExamples of these products are

I flexible Gas fired power plants Essentially a path dependentoption on the clean spark spread the spread between theelectricity price on one side and on the gas and CO2 certificatesprice on the other side

I Hydro storage Option on time spreads (spread of forwards withdifferent maturities) spikes and seasonality of the electricityprices

I Gas storages Options on time spreads and spikes of the gasmarket

I Swing contracts Options to choose the time of delivery within agiven period

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Outline

Electricity and related MarketsMarket introduction

Electricity Spot pricesElectricity spot price formationSeasonality

Some electricity price modelsStructural ModelsSpot factor ModelsForward Models

X-Border CapacitiesProduct descriptionLower bound for valuation

Other products

Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Conclusion

I We have discussed statistical properties of electricity spot andforward prices and approaches how to model them

I We have discussed existing models for cross-border transmissionright valuations which basically boil down to valuing a spreadoption However so far there are no reduced form modelsavailable which are capable to reproduce price spreads asobserved Especially the existing reduced form models do notreproduce the large frequency at which spot prices are equal forneighbouring markets Additionally they do not account for theregime switches that can be observed

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

References I

ADAMEC MAREK INDRAKOVA MICHAELA amp PAVLATKA PAVEL 2009Market coupling and price coordination between power exchangesIn 10th IAEE European Conference Vienna Austria vol 7

BARLOW M T 2002 A DIFFUSION MODEL FOR ELECTRICITYPRICES Mathematical Finance 12(4) 287ndash298

BENTH FRED ESPEN KHOLODNYI VALERY A amp LAURENCE PETER2013 Quantitative Energy Finance Modeling Pricing and Hedgingin Energy and Commodity Markets Auflage 2014 edn New YorkSpringer

BJERKSUND PETTER RASMUSSEN HEINE amp STENSLAND GUNNAR2010 Valuation and Risk Management in the Norwegian ElectricityMarket Pages 167ndash185 of BJOslashRNDA ENDRE BJOslashRNDA METTEPARDALOS PANOS M amp ROumlNNQVIST MIKAEL (eds) EnergyNatural Resources and Environmental Economics EnergySystems Springer Berlin Heidelberg

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

References II

CARMONA RENEacute COULON MICHAEL amp SCHWARZ DANIEL 2013Electricity price modeling and asset valuation a multi-fuel structuralapproach Mathematics and Financial Economics 7(2) 167ndash202

CORNLUSSE BERTRAND 2014 (10) How the European day-aheadelectricity market works

HEATH DAVID JARROW ROBERT amp MORTON ANDREW 1992 BondPricing and the Term Structure of Interest Rates A NewMethodology for Contingent Claims Valuation Econometrica 60(1)pp 77ndash105

KIESEL RDIGER SCHINDLMAYR GERO amp BRGER REIK H 2009 Atwo-factor model for the electricity forward market QuantitativeFinance 9(3) 279ndash287

KIESEL RUEDIGER amp KUSTERMANN MICHAEL MARTIN 2015 (10)Structural Models for Coupled Electricity Markets

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

References III

KOEKEBAKKER STEEN amp OLLMAR FRIDTHJOF 2005 Forward curvedynamics in the Nordic electricity market Managerial Finance31(6) 73ndash94

LONGSTAFF FRANCIS A amp SCHWARTZ EDUARDO S 2001 ValuingAmerican Options by Simulation A Simple Least-SquaresApproach Review of Financial Studies 14(1) 113ndash147

MAHRINGER STEFFEN FSS ROLAND amp PROKOPCZUK MARCEL2015 (6) Electricity Market Coupling and the Pricing ofTransmission Rights An Option-based Approach University ofStGallen School of Finance Research Paper No 201512

MARGRABE WILLIAM 1978 The Value of an Option to Exchange OneAsset for Another The Journal of Finance 33(1) 177ndash186

MEYER-BRANDIS THILO amp TANKOV PETER 2008 Multi-factorJump-Diffusion Models of Electricity Prices International Journal ofTheoretical and Applied Finance 11(05) 503ndash528

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

References IV

SAMULESON PAUL A 1965 Proof That Properly Anticipated PricesFluctuate Randomly Industrial Management Review 6(2) 41ndash49

WOBBEN MAGNUS DIECKMANN BIRGIT amp REICHMANN OLEG2012 Valuation of physical transmission rights - An analysis ofelectricity cross-border capacities between Germany and theNetherlands Energy Policy 42 174 ndash 180

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion

Disclaimer

The views represented herein are the author own views and do notnecessarily represent the views of Axpo Trading or its affiliates

• Electricity and related Markets
• • Market introduction
  • • Electricity Spot prices
    • • Electricity spot price formation
      • Seasonality
      • • Some electricity price models
        • • Structural Models
          • Spot factor Models
          • Forward Models
          • • X-Border Capacities
            • • Product description
              • Lower bound for valuation
              • • Other products
                • Conclusion