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An Introduction to Derivative Markets and Securities
Innovative Financial InstrumentsDr. A. DeMaskey
Chapter 11
Learning ObjectivesQuestions to be answered: What are derivative securities? What are the basic types of derivative securities and the
terminology associated with them? What are the similarities and differences in the payoff
structures created by each of the derivative instruments? How are forward contracts, put options and call options
related? What are the uses of derivative contracts?
Derivative Instruments
The value depends directly on, or is derived from, the value of another security or commodity, called the underlying asset.
Forward and Futures contracts are agreements between two parties - the buyer agrees to purchase an asset from the seller at a specific date at a price agreed to now.
Options offer the buyer the right without obligation to buy or sell at a fixed price up to or on a specific date.
Why Do Derivatives Exist?
Assets are traded in the cash or spot market. It is sometimes advantageous to enter into a
transaction now with the exchange of the asset and payment taking place at a future time.
Risk shifting Price formation Investment cost reduction
Characteristics of Derivative Instruments
Forward contracts are the right and full obligation to conduct a transaction involving another security or commodity - the underlying asset - at a predetermined date (maturity date) and at a predetermined price (contract price). This is a trade agreement.
Futures contracts are similar, but subject to margin requirements and daily settlement.
Options give the holder the right to either buy or sell a specified amount of the underlying asset at a specified price within a specified period of time.
Forward Contracts
Buyer is long, seller is short Contracts have negotiable terms and
are traded in the OTC market Subject to credit risk or default risk No payments until expiration Agreement may be illiquid
Payoff Structure to Long and Short Forward Positions
St
Profit
Loss
F0,T
Long Forward
Short Forward
LongGain
ShortGain
ShortLoss
LongLoss
S1 S20
Futures Contracts
Standardized terms Central market (futures exchange) More liquidity Less liquidity risk due to initial margin Daily settlement called “marking-to-
market”
Option Contracts
Holder vs. Grantor Call Option vs. Put
Option Exercise or Strike
Price Premium
American Option vs. European Option
At-The-Money Option In-The-Money Option Out-Of-The Money
Option
Option Pricing and Valuation
An option’s value consists of two parts:– Intrinsic Value– Time Value
Intrinsic Value is the amount by which an option is in-the-money
Time Value is the amount by which an option’s value exceeds its intrinsic value
To Illustrate: Suppose the current stock price is 50. The premium on a
call option with an exercise price of 48 is $5.25.– What is the intrinsic value (IV)? – What is the time value (TV)?
E
Time value
Call Option Value
Spot RateIntrinsic value
Total value of option
Out-of-the-money In-the-money
Basic Pricing Relationships Call options are always worth at least the intrinsic
value. The lower the exercise price, the greater the call
option’s premium. The longer the time to expiration, the greater the
value of any option. The greater the volatility of the underlying asset,
the greater the value of any option. American options are at least as valuable as
European options.
Option Pricing Relationships
Factor Call Option Put Option
Stock price + -
Exercise price - +
Time to expiration + +
Interest rate + -
Volatility of underlying asset + +
Where: + = positive or direct relationship - = negative or inverse relationship
Profits to Buyer of Call Option
40 50 60 70 80 90 100
1,000
500
0
1,500
2,000
2,500
3,000
(500)
(1,000)
Exercise Price = $70
Option Price = $6.125
Profit from Strategy
Stock Price at Expiration
Profits to Seller of Call Option
40 50 60 70 80 90 100
(1,000)
(1,500)
(2,000)
(500)
0
500
1,000
(2,500)
(3,000)
Exercise Price = $70
Option Price = $6.125
Stock Price at Expiration
Profit from Strategy
Breakeven price
X=70
Limited Gain
PotentiallyUnlimited Loss
Profits to Buyer of Put Option
40 50 60 70 80 90 100
1,000
500
0
1,500
2,000
2,500
3,000
(500)
(1,000)
Exercise Price = $70
Option Price = $2.25
Profit from Strategy
Stock Price at Expiration
Profits to Seller of Put Option
40 50 60 70 80 90 100
(1,000)
(1,500)
(2,000)
(500)
0
500
1,000
(2,500)
(3,000)
Exercise Price = $70
Option Price = $2.25
Stock Price at Expiration
Profit from Strategy
Limited Gain
X=70PotentiallyLimited Loss
Breakeven price
Investing with Derivative Securities
Forward contract– does not require front-end payment– requires future settlement payment
Option contract– requires up front payment– allows but does not require future
settlement payment
Put-Call-Spot Parity
A. Net Portfolio Investment at Initiation (Time 0)PortfolioLong 1 WZY StockLong 1 Put OptionShort 1 Call OptionNet Investment
S0
P0,T
-C 0,T
S0 + P0,T - C 0,T
B. Portfolio Value at Option Expiration (Time T)PortfolioLong 1 WZY StockLong 1 Put OptionShort 1 Call Option
Net Position
If ST XST
(X - ST)0
X
If ST > XST
0-(ST - X)
X
Put-Call-Spot Parity
The net position is a guaranteed contract; that is, it is riskfree.
Since the riskfree rate equals the T-bill rate, the no-arbitrage condition can be shown as:(long stock)+(long put)+(short call)=(long T-bill)
TTT RFR
XCPS
)1(,0,00
Application of Put-Call Parity
If securities are properly valued, the net position has a value of zero.
Put-call-spot parity can be used to check if calls and puts are properly priced relative to each other.
Any mispricing of calls and puts offer arbitrage opportunities.
Creating Synthetic Securities Using Put-Call-Spot Parity
A riskfree portfolio could be created by combining three risky securities:– a stock – a put option,– and a call option
With the Treasury-bill as the fourth security, any one of the four may be replaced with combinations of the other three
Replicating a Put Option
A. Net Portfolio Investment at Initiation (Time 0)PortfolioLong 1 T-BillShort 1 XYZ StockLong 1 Call OptionNet Investment
X(1 + RFR)-T
-S0
C 0,T
X(1 + RFR)-T - S0 + C 0,T
B. Portfolio Value at Option Expiration (Time T)PortfolioLong 1 T-BillShort 1 XYZ StockLong 1 Call Option
Net Position
If ST XX
- ST
0
X - ST
If ST > XX-ST
(ST - X)
0
Adjusting Put-Call Spot Parity For Dividends
If a stock pays a dividend, DT, immediately prior to expiration of the options, put-call parity is modified as follows:
TT
TT RFR
DXCPS
)1(,0,00
TTTTT
RFR
XCP
RFR
DS
)1()1( ,0,00
or
Put-Call-Forward Parity
Instead of buying stock, take a long position in a forward contract to buy stock.
Supplement this transaction by purchasing a put option and selling a call option, each with the same exercise price and expiration date.
This reduces the net initial investment compared to purchasing the stock in the spot market.
Put-Call-Forward Parity
A. Net Portfolio Investment at Initiation (Time 0)PortfolioLong 1 Forward ContractLong 1 Put OptionShort 1 Call OptionNet Investment
0P0,T
-C 0,T
P0,T - C 0,T
B. Portfolio Value at Option Expiration (Time T)PortfolioLong 1 Forward ContractLong 1 Put OptionShort 1 Call Option
Net Position
If ST XST - F0,T
(X - ST)0
X - F0,T
If ST > X
0-(ST - X)
ST - F0,T
X - F0,T
Put-Call-Forward Parity
If this condition does not hold, then there are opportunities for arbitrage.
If the stock pays a dividend at times T, the condition becomes:
TT
TT RFR
FXCP
)1(,0
,0,0
TT
TT
RFR
F
RFR
DS
)1()1(,0
0
Restructuring Asset Portfolios with Forward Contracts
Tactical asset allocation to time general market movements instead of company-specific trends.
Direct Method:– Sell stock in open market and buy T-bills
Indirect Method:– Short forward contracts against a long position in
underlying asset Benefits:
– Quicker and cheaper– Neutralizes risk of falling stock price– Converts beta of stock to zero
Dynamics of Hedge
EconomicEvent
ActualStockExposure
DesiredForwardExposure
Stockprices fall Loss Gain
Stockprices rises Gain Loss
ff
Protecting Portfolio Value with Put Options
Protective Puts– Hedge potential drop in value of underlying
asset– Keep from committing to sell if price rises– Asymmetric hedge
Portfolio Insurance– Hold the shares and purchase a put option, or– Sell the shares and buy a T-bill and a call
option
Dynamics of Hedge
EconomicEvent
ActualStockExposure
DesiredHedgeExposure
Stockprices fall Loss Gain
Stockprices rises Gain No Loss
ff
The InternetInvestments Online
www.cboe.com
www.cbot.com
www.cme.com
www.cme.com/educational/hand1.htm
www.liffe.com
www.options-iri.com