© 2004 South-Western Publishing 1

Chapter 15

Other Derivative Assets

2

Futures Options

CharacteristicsSpeculators and Hedging Early exercise of futures optionsPricing Futures OptionsDeltas and Implied volatility

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Characteristics

Are futures options “uniquely worthless”? Futures options give users of the futures

market an enhanced ability to tailor their risk/return exposure to individual needs

Futures options provide an opportunity for the speculator to avoid the potentially unlimited losses associated with futures contracts

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Characteristics (cont’d)

Futures options are relatively new– Non-agricultural futures since 1982– Agricultural futures since 1984

Commodity Futures Trading Commission Act of 1974– Futures options must not be “contrary to the

public interest”– Futures options must serve legitimate hedging

purposes

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Characteristics (cont’d)

Futures options are no different from listed options– Futures calls give the right to go long– Call writer has the obligation to go short if the

call holder exercises– Futures puts give the right to go short– Put writer has the obligation to go long if the put

holder exercises

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Characteristics (cont’d)

The underlying security is the futures contract, not the physical commodity represented by the futures contract

The option holder decides if and when to exercise

Exercise of a futures call does not result in delivery of the underlying commodity

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Characteristics (cont’d)

Futures Prices

S&P 500 Index

Open

MAR 1138.30

JUN 1137.00

SEP ….

DEC 1139.00

S&P 500 Index

Calls

Strike Price

FEB MAR APR

1140 11.60 22.50 30.20

1150 6.60 17.00 24.80

1160 3.30 12.60 20.00

1170 1.45 9.00 15.80

1180 0.65 6.20 12.40

Futures Options Prices

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Characteristics (cont’d)

Futures Prices

Puts

FEB MAR APR

8.40 19.30 27.90

13.40 23.80 32.50

20.10 29.40 37.60

28.20 35.80 ….

37.40 …. ….

S&P 500 Index

Open

MAR 1138.30

JUN 1137.00

SEP ….

DEC 1139.00

Futures Options Prices

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Characteristics (cont’d)

Like other puts and calls, futures options have both intrinsic value and time value

Expiration– The option month refers to the futures contract

delivery month– Depending on the commodity, the option may

expire on a specific date in the preceding month– The actual expiration date varies by commodity– Some futures options have a serial expiration

feature

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Speculating With Futures Options

Speculation principles for futures options are the same as for equity options

Buying futures options involves a predetermined, known, and limited maximum loss, just as with options on other assets– The option premium is the most the option

buyer can lose

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Speculating With Futures Options (cont’d)

Money At Risk Example

In early September, a speculator anticipates lower demand for soybeans and anticipates a drop in the price of soybeans. She decides to buy a put option on soybean futures. Specifically, she purchases 3 APR 8300 puts at a listed price of 25.25 cents. The money at risk is

3 contracts x 5,000bu/contract x $0.2525/bu = $3,787.50

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Hedging With Futures Options

There are as many ways to hedge with futures options as there are with equity or index options– Any hedge serves to limit risk with some

tradeoff in potential return– In the commodities market, there can be several

levels of hedging

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Hedging With Futures Options (cont’d)

Hedging Example

William Bob operates a 1,500-acre farm in the midwest and plans on harvesting 50,000 bushels of soybeans. To hedge price risk, Bob could go short 10 soybean contracts, covering 50,000 bushels. However, to protect himself against unexpected problems with the crop (such as tornadoes), Bob could hedge by only going short 9 soybean contracts. This reduces the inconvenience and cost of having to either close out some contracts at a financial loss or acquire soybeans in the cash market to deliver against the short contracts.

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Speculators and Hedging

Futures options are particularly useful to speculators of interest rate of stock index futures– If a speculator buys an S&P 500 index futures

contract, a market decline results in a reduced account balance as the contract is marked to market each day

– Puts on the S&P futures would provide some protection against the potentially large losses

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Early Exercise of Futures Options

Listed call options on equity securities or indexes will not normally be exercised early– This would result in an abandonment of the

remaining time value of the option

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Early Exercise of Futures Options (cont’d)

With futures options, there are circumstances in which it is optimal to exercise a call early– E.g., exercising a call allows the speculator to

go long in futures and to earn interest with the futures contract

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Pricing Futures Options

Futures option pricing model Disposing of valuable options Futures option deltas Implied volatility

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Futures Option Pricing Model

Black’s futures option pricing model for European call options:

Tab

T

TK

F

a

bKNaFNeC RT

and

2ln

where

)()(2

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Futures Option Pricing Model (cont’d)

Black’s futures option pricing model for European put options:

Alternatively, value the put option using put/call parity:

)()( aFNbKNeP RT

)( KFeCP RT

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Disposing of Valuable Options

The holder of a futures option has three alternatives:– Keep the option– Exercise the option– Sell the option

The risk of holding onto the option is that prices may move adversely

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Disposing of Valuable Options (cont’d)

The early exercise of option is normally suboptimal– Deep-in-the-money options have little time value

and it is often advantageous to exercise them early

Selling the option has the merit of capturing the remaining time value and converts the intrinsic value to cash

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Futures Option Deltas

Slightly different from delta for equity or index options– Call delta:

– Put delta:

)(aNe RT

)( bNe RT

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Implied Volatility

Implied volatility is the standard deviation of returns that will cause the pricing model to predict the actual option premium

Calculating implied volatility must be done via trial and error

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Summary

New Derivatives combining options and futures Pricing includes the extra time gained Deltas (C&P) are different from that of an

option (do not add up to one!) Research on Implied volatility in Financial

Modeling!