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

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