l8 Weather Derivatives

Copyright SDA Bocconi, protocollo xxxx

Lecture 8: Weather Derivatives

Derivatives in Corporate Finance

Alonso Pea

SDA Bocconi, Intermediazione Finanziaria e Assicurazioni

Copyright SDA Bocconi, protocollo xxxx 2 Copyright SDA Bocconi 2007

2

Part 1:

Introduction

Part 2:

Examples of Weather Derivatives

Part 3:

Modelling Weather Derivatives

Part 4:

Case Study: United Nations World

Food Programme

Contents


Part 1: Introduction


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Weather Risk The study of derivatives entails understanding risk. We have covered a lot of different types of risks, the main ones being market risk arising from interest rates, exchange rates, commodity prices, and stock prices, and also credit risk. In this lecture we introduce derivatives on one of the most interesting and important sources of risk: the weather.

Introduction Weather Derivatives*

*These selections are from: Don M. Chance, Essays in Derivatives: Risk-Transfer Tools and Topics Made Easy, Wiley, 2 edition, 2008. Essay 20.


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Weather and Business It is not difficult to think of the types of businesses that benefit or are hurt by the weather. Even a child's lemonade stand benefits from hot weather. Imagine beer and soda companies benefiting from hot weather and companies that sell hot chocolate and cocoa benefiting from cold weather.

Introduction Weather Derivatives


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Weather and Business Ski resorts, vacation properties, the travel industry, and clothing manufacturers are good examples of companies whose business is partially and in some cases primarily driven by the weather. On a larger scale, public utilities and airlines are heavily influenced by the weather. The derivatives industry has recognized the importance of weather by creating a class of products known as weather derivatives.



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Weather data Weather is an excellent variable on which risk can be measured. Weather is typically a highly quantifiable variable. In fact, we are inundated with information on weather, and virtually every adult and many children have a modest understanding of it. Statistical information is abundant, and lengthy series of historical data exist on temperatures and precipitation for localities all over the world.



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Weather data Internert sites: www.weather.com weather.yahoo.com it is a relatively simple task to obtain qualitative and quantitative information on weather anywhere on the planet. Insurance companies, which have provided policies against weather-related damage for a long time, have extensive information about the historical consequences of severe weather.



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Weather data: temperature The derivatives industry uses temperature as the underlying of various contracts by means of two related concepts: the heating degree-day (HDD) and the cooling degree-day (CDD). A heating degree-day is the number of degrees the average temperature in a given day is below 65 degrees Fahrenheit (18.33 Celsius). A cooling-degree day is the number of degrees the average temperature in a given day is above 65.



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If the average temperature in a day is 63 degrees, the weather is measured as two heating degree-days. If the average temperature in a day is 67 degrees, the measure is two cooling degree-days. A heating-degree day is, thus, a rough proxy for the necessity to provide heat to obtain a comfortable temperature, while a cooling degree-day is a rough proxy for the necessity to provide coolness to obtain a comfortable temperature.



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The notion of a heating or cooling degree-day provides a reasonable underlying for weather derivative contracts. Consider one six-month call option on cooling degree-days. Let us say the buyer expects that the average temperature over the next month (assume 30 days) will be 72 degrees, which is 7 cooling degree-days on average. Then as a rough choice for the exercise price, the buyer chooses 210 i.e. 30 x 7 = 210.



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The buyer pays the premium and receives a call option that will pay at expiration a certain amount of money, call it m, for every cooling degree-day over 210. If the total number of cooling degree-days is less than 210, the option expires out-of-the-money. If the buyer is interested in benefiting from lower-than-expected temperatures, she would buy a put on heating degree-days and benefit if the number of heating degree days is lower than the chosen strike.



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Of course, determining m is the really difficult part. The option buyer needs to know what financial loss she expects on her business for each degree above 65 is the average temperature. These estimates, however, should be fairly well understood by anyone in business. Indeed, the child with the lemonade stand probably knows to make a few more liters of lemonade on those hot days and a few less on cooler ones.



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Other forms of weather derivatives have been created on such measures as rainfall and snowfall. Dealers that make these markets typically have an expertise in these markets. Often this expertise is purchased by buying another company or by hiring personnel, such as weather experts.



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While most weather derivatives contracts are over the counter, exchange-traded weather derivatives have existed since the first ones were launched in 1999 at the Chicago Mercantile Exchange (CME). These futures and options on futures are based on average temperatures in 18 U.S. and 15 non-U.S. cities. The CME has also offered futures and options on futures on an index of hurricane intensity, the number of days of frost, and the number of days of snowfall.



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In spite of great efforts, however, the CME contracts have not

garnered much volume.

A few years ago the Chicago Board of Trade offered derivatives

on insurance claims arising from hurricanes and

earthquakes.

These contracts drew a great deal of acclaim and attention, in

particular from academics keen on deriving pricing formulas.

But after all was said and done, these contracts did not draw

much actual trading volume.



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While some tout the weather and environmental derivatives

markets as innovative and successful, I can agree only on the first

point.

They certainly are innovative, striking at the very heart of certain

significant risks encountered by many businesses. Nonetheless,

their innovative nature has in some sense been their bane.

Weather derivatives may be innovative, but they are completely

out of the traditional box of derivative products and therein lie

some problems.



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Pricing weather derivatives typically occurs in a much

more challenging manner.

Usually the underlying variable and its financial consequences

are forecasted, and a price is based on a discounting of the

expected payoffs.

Pricing methodologies are discussed later.



Part 2: Examples


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1997: the first widely publicised deal in the US took place

between Enron and Koch Energy, referenced to the Milwaukee

winter season; in September 1998, the first European deal

between Enron and Scottish Power was made.

1999: Canadian snowmobile maker Bombardier entered into a

snowfall contract with Enron. Bombardier would pay a

US$1,000 rebate to customers if snowfall levels did not reach

half that of the previous three years. It funded this potential

liability by purchasing snowfall digital floors structured in each

major market where the promotion was offered (44 cities).

Examples Corporate users


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2001: London-based The White Swan pub entered into a

temperature contract with SocGen. Payment was triggered

by the number of cold Fridays and Saturdays during the

April-July period. In particular, the pub would receive

compensation if there are too few such days where the

temperature was above 14C in April and 18C in May, and if

there are too many such days where the temperature was

below 18C in June and 20C in July. White Swan estimated

that it stood to lose in excess of 15,000 per day that was

too cold to drink outside.



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2001: the city of Sacramento in California entered into a

precipitation contract with Aquila Energy. During droughts,

Sacramento was to get less of its electricity from hydroelectric

dams and pay higher prices for power on the open market. To

ease the pain of high-cost droughts, the Sacramento

Municipal Utility District (SMUD) entered a five-year contract

with Aquila.



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2001: Japan's Imaoka Corporation, a manufacturer of sore

throat lozenges, was one of the first companies to purchase

a weather derivative referenced to humidity, aimed at

protecting revenues in case of an unusually humid winter. For

Imaoka, sales often drop during the country's hot summer

months (the soaring humidity levels lessening incidences of

dry raspy coughs among the Japanese population).



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2002: Gut Apeldor golf club in Hennstedt, Germany, bought

a precipitation derivative that covered it from the risk of heavy

rain keeping golfers away (the weather in 2001 had been

miserable in that respect). The managers of the club decided

that they could put up with 50 rainy days from May to

September.



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2004: Corney & Barrow (C&B), which owns a: chain of

wine bars in the City of London, has closed a weather

derivatives deal with US energy giant Enron - the first such

undertaking by a non-energy company in the UK. The deal

was brokered by Speedwell Weather, a division of the UK-

based bond software company Speedwell Associates.



Part 3: Modelling


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The lack of a single universal pricing model is a major

hurdle to the growth of the weather derivatives market.

It prevents participants from talking in the same language,

with each market maker essentially developing its own

pricing methodologies (which they, predictably, may not be

too willing to share with outsiders).

Modelling Pricing weather derivatives


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If a generally recognized pricing model were developed,

this could greatly improve market transparency and

would most likely enhance the number of entrants.

Just as the Black-Scholes breakthrough has been a key

driving factor of the explosive growth experienced by, among

others, the equity and currency options markets in the last 30

years, the weather market needs a common reference.



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Why is it difficult to come up with a standard weather-

derivatives pricing formula?

Plainly stated, because the Black-Scholes framework

cannot be used in this context.

While Black-Scholes modeling may be the standard approach

for options pricing in many other derivatives markets, applying

it to weather derivatives is hazardous because there is no

underlying tradable asset.



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Another obstacle lies in the fact that the mathematics behind

Black-Scholes cannot be applied to the weather market.

Black-Scholes assumes that the underlying follows a random

walk without mean reversion where the volatility increases

with time.

In practice, weather shows mean-reverting tendencies

(tendencies to go back to its historical levels) and is

reasonably predictable, at least in the short term.

Black-Scholes can be modified to take into account mean-

reversion.



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In light of these modeling difficulties, practitioners have opted

for two more hands-on: historical analysis and simulation.

Historical analysis, or "burn analysis", makes use of past

weather data to determine the fair value of the option. This

method is quite straightforward, needing only the collection of

historical time series and calculating what would have been

the payoff for a particular option on each past date. The price

of the option should then equal the average of all those

payoffs.



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A drawback associated with burn analysis is that it is

totally data-dependent, that is, it makes a difference how

far back in time we go to calculate the average historical

payoff of the option.

Using, say, 10-years data will most likely yield very different

results from using 50-years data. A recent study of New York

City's weather derivatives market found the following

diverging figures for CDD, (three summer months) and

heating HDD, (three winter months), depending on the time

series considered.



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Monte Carlo simulation seems to be the most commonly used

method for pricing weather derivatives.

It entails generating, with the help of a computer, a large

number of simulated random future weather scenarios to

determine possible option payoffs.

The option premium would then be the discounted average of

all those possible payoffs.



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The drawback associated with simulation is, of course,

how to generate the future scenarios in the first place.

The answer lies in choosing an appropriate process for

the underlying (temperature changes beyond an index,

rainfall, wind speed, etc). Temperature is mean reverting

and not a random walk (volatility stays within a

reasonable range through time)

Probabilistic process used for simulation purposes should

take those aspects into account.



Part 4: Case Study


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Source: http://www.wfp.org/node/598

Case Study UN World Food Programme


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ADDIS ABABA The United Nations

World Food Programme announced today

that AXA RE has been awarded the

world s first insurance contract for humanitarian emergencies. The contract

provides US $7 million in contingency

funding in a pilot scheme to provide

coverage in the case of an extreme

drought during Ethiopia s 2006 agricultural season.

So much of our work is like triage doing



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The humanitarian emergency insurance contract might, in the future, offer us a

way of insuring against these massive

losses before they spell destitution for

millions of families, said Morris.

As a worldwide leader in Financial Protection and one of the pioneers of

weather cover through its subsidiary AXA

RE, AXA is happy to provide its financial

expertise in



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This contract heralds the beginning of what may be an entirely new way of financing

natural disaster aid, said Richard Wilcox, Director of Business Planning at the World

Food Programme . With this pilot, developed together with the World Bank

Commodity Risk Management Group, we

are testing whether it is possible to insure

against the devastation

caused by extreme drought.

The policy, a derivative based upon a



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the likelihood of widespread crop

failure. While the experimental pilot

transaction only provides a small amount

of contingency funding, the model has

been designed on the basis of the

potential losses that 17 million poor

Ethiopian farmers risk should an extreme

drought arise.

The policy complements recent UN

moves towards greater effectiveness



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Some disasters especially conflict and displacement are harder to predict and

faster to unfold, so we will continue to

need untied contingency funds. Risks

such as drought, however, can also be

managed effectively under the type of

contract we have just signed with AXA

Re , explained Wilcox.

Transferring weather risks from poor

countries like Ethiopia into the

international risk market on a larger



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The portfolio effect of bringing emergency aid into the international risk

markets is a win- win for developed and

developing countries. Wit h this deal

WFP is making a bold move towards

more equitable and effective international

risk management , said Robert Shiller, Professor of Financial Economics at Yale

University and author of The New Financial Order: Risk in the 21st

Century.



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We have shown that the reinsurance sector can have an important role to

play in effective financing for

responses to natural disasters in

developing countries. Now the

industry itself should take up the

challenge to provide effective products

to developing countries and the aid

community.

Together we can build this innovation



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References:

WFP is the world's largest humanitarian

agency: each year, we give food to an

average of 90 million poor people to meet

their nutritional needs, including 61

million hungry children, in at least 80 of

the world's poorest countries. WFP -- We

Feed People.

AXA Group is a worldwide leader in

financial protection. We support 50


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