Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 12: Options on Futures My option gave me the right to a futures contract for that much

Copyright © 2001 by Harcourt, Inc. All rights reserved.

1

Chapter 12: Options on Futures

My option gave me the right to a futures contract for that My option gave me the right to a futures contract for that much hog [30,000 pounds] until October. Considering the much hog [30,000 pounds] until October. Considering the average size of a hog, which I figured to be 500 pounds, this average size of a hog, which I figured to be 500 pounds, this gave me a potential controlling interest in 600 animals. gave me a potential controlling interest in 600 animals. Right then, I vowed to eat more pork chops and bacon, and Right then, I vowed to eat more pork chops and bacon, and to call my friends to beg them to do the same.to call my friends to beg them to do the same.

John RothchildJohn Rothchild

A Fool and His MoneyA Fool and His Money

19971997


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Important Concepts in Chapter 12 The concept of an option where the underlying is a futures The concept of an option where the underlying is a futures

contract and comparisons to options where the underlying is a contract and comparisons to options where the underlying is a spot instrumentspot instrument

Basic principles of pricing options on futuresBasic principles of pricing options on futures The early exercise possibilities for American options on The early exercise possibilities for American options on

futuresfutures The Black and binomial pricing models for options on futuresThe Black and binomial pricing models for options on futures Trading strategies of buying calls, buying puts and selling Trading strategies of buying calls, buying puts and selling

covered callscovered calls To compare options on futures with options on the spotTo compare options on futures with options on the spot


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Characteristics of Options on Futures

Options where exercise establishes either a long or short Options where exercise establishes either a long or short position in a futures contract at the exercise priceposition in a futures contract at the exercise price Exercise of long (short) call establishes a long (short) Exercise of long (short) call establishes a long (short)

futures.futures. Exercise of a long (short) put establishes a short (long) Exercise of a long (short) put establishes a short (long)

futures.futures. Also called commodity options or futures options.Also called commodity options or futures options.


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Characteristics of Options on Futures (continued) Example from January 31, 2000. June Treasury bond futures Example from January 31, 2000. June Treasury bond futures

call option with exercise price of 90.call option with exercise price of 90. Right to buy June futures at 90Right to buy June futures at 90 Costs 3 15/64 or 3.234375, which is $3,234.75.Costs 3 15/64 or 3.234375, which is $3,234.75. If exercised when futures = 93, holder establishes long If exercised when futures = 93, holder establishes long

futures position at 90, which is immediately marked to futures position at 90, which is immediately marked to market at 93 for a $3,000 credit to margin account.market at 93 for a $3,000 credit to margin account.

Long put works similarly but establishes short futures Long put works similarly but establishes short futures position. Priced at 1 18/64 or $1,281.25.position. Priced at 1 18/64 or $1,281.25.

Note: expiration can be same month as futures or earlier, Note: expiration can be same month as futures or earlier, depending on the contract.depending on the contract.


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Characteristics of Options on Futures (continued) Many types of options on futures are very actively traded.Many types of options on futures are very actively traded.

See See Figure 12.1, p. 507Figure 12.1, p. 507 for annual volume. for annual volume. See See Figure 12.2, p. 508Figure 12.2, p. 508 for market share by contract for market share by contract

group. Financials are dominant.group. Financials are dominant. See See Table 12.1, p. 12.1Table 12.1, p. 12.1 for breakdown by exchange. for breakdown by exchange.

See See Figure 12.3, p. 510Figure 12.3, p. 510 for for The Wall Street JournalThe Wall Street Journal quotes.quotes.

See See Table 12.2, p. 511Table 12.2, p. 511 for list of contracts trading. for list of contracts trading. See See Table 12.3, p. 512Table 12.3, p. 512 for most active contracts. for most active contracts.


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Pricing Options on Futures

The Intrinsic Value of an American Option on FuturesThe Intrinsic Value of an American Option on Futures Minimum value of American call on futuresMinimum value of American call on futures

CCaa(f(f00,T,X) ,T,X) Max(0,f0 - X)

Minimum value of American put on futuresMinimum value of American put on futures PPaa(f(f00,T,X) ,T,X) Max(0,X - f0)

Difference between option price and intrinsic value is Difference between option price and intrinsic value is time value.time value.


7

Pricing Options on Futures (continued)

The Lower Bound of a European Option on FuturesThe Lower Bound of a European Option on Futures For calls, construct two portfolios. See For calls, construct two portfolios. See Table 12.4, p. Table 12.4, p.

513513 Portfolio A dominates Portfolio B soPortfolio A dominates Portfolio B so

CCee(f(f00,T,X) ,T,X) Max[0,(f0 - X)(1+r)-T]

Note that lower bound can be less than intrinsic value Note that lower bound can be less than intrinsic value even for calls.even for calls.

For puts, see For puts, see Table 12.5, p. 514Table 12.5, p. 514.. Portfolio A dominates Portfolio B soPortfolio A dominates Portfolio B so

PPee(f(f00,T,X) ,T,X) Max[0,(X - f0)(1+r)-T]


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Put-Call Parity of Options on FuturesPut-Call Parity of Options on Futures Construct two portfolios, A and B.Construct two portfolios, A and B. See See Table 12.6, p. 516Table 12.6, p. 516.. The portfolios produce equivalent results. Therefore they must The portfolios produce equivalent results. Therefore they must

have equivalent current values. Thus,have equivalent current values. Thus, PPee(f(f00,T,X) = C,T,X) = Cee(f(f00,T,X) + (X - f,T,X) + (X - f00)(1+r))(1+r)-T-T..

Compare to put-call parity for options on spot:Compare to put-call parity for options on spot: PPee(S(S00,T,X) = C,T,X) = Cee(S(S00,T,X) - S,T,X) - S00 + X(1+r) + X(1+r)-T-T.. If options on spot and options on futures expire at same If options on spot and options on futures expire at same

time, their values are equal, implying ftime, their values are equal, implying f00 = S = S00(1+r)(1+r)TT, which , which

we obtained in Chapter 9.we obtained in Chapter 9.


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Early Exercise of Call and Put Options on FuturesEarly Exercise of Call and Put Options on Futures Deep in-the-money call may be exercised early becauseDeep in-the-money call may be exercised early because

behaves almost identically to futuresbehaves almost identically to futures exercise frees up funds tied up in option but requires no exercise frees up funds tied up in option but requires no

funds to establish futuresfunds to establish futures minimum value of European futures call is less than value minimum value of European futures call is less than value

if it could be exercisedif it could be exercised See See Figure 12.4, p. 518Figure 12.4, p. 518.. Similar arguments hold for putsSimilar arguments hold for puts Compare to the arguments for early exercise of call and put Compare to the arguments for early exercise of call and put

options on spot.options on spot.


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Options on Futures Pricing ModelsOptions on Futures Pricing Models Black model for pricing European options on futuresBlack model for pricing European options on futures

Tdd

T

T/2/X)ln(fd

where

)]XN(d)N(d[feC

12

20

1

210Trc


11


Options on Futures Pricing Models (continued)Options on Futures Pricing Models (continued) Note that with the same expiration for options on spot Note that with the same expiration for options on spot

as options on futures, this formula gives the same price.as options on futures, this formula gives the same price. ExampleExample

See See Table 12.7, p. 520Table 12.7, p. 520.. Software for Black-Scholes can be used by inserting Software for Black-Scholes can be used by inserting

futures price instead of spot price and risk-free rate for futures price instead of spot price and risk-free rate for dividend yield. Note why this works.dividend yield. Note why this works.

For putsFor puts

)]N(d[1ef)]N(d[1XeP 1Tr

02Tr cc


12


Options on Futures Pricing Models (continued)Options on Futures Pricing Models (continued) Note how the binomial model can be used.Note how the binomial model can be used. See See Figure 12.5, p. 522Figure 12.5, p. 522 for paths of spot and futures for paths of spot and futures

price for two-period example with strike of 50.price for two-period example with strike of 50. Futures option prices at expiration (same as spot)Futures option prices at expiration (same as spot)

Max(0,156.25 - 100) = 56.25Max(0,156.25 - 100) = 56.25 Max(0,100 - 100) = 0.0Max(0,100 - 100) = 0.0 Max(0,64 - 100) = 0.0Max(0,64 - 100) = 0.0


13


Options on Futures Pricing Models (continued)Options on Futures Pricing Models (continued) Option prices at time 1 (futures is 133.75) Option prices at time 1 (futures is 133.75)

[56.25(.6) + 0.0(.4)]/1.07 = 31.54[56.25(.6) + 0.0(.4)]/1.07 = 31.54• If American, intrinsic value is 133.75 - 100 = 33.75. If American, intrinsic value is 133.75 - 100 = 33.75.

So exercise early.So exercise early. If futures is 85.60, option is worth nothingIf futures is 85.60, option is worth nothing

At time 0 option price isAt time 0 option price is [33.75(.6) + 0.0(.4)] /1.07 = 18.93[33.75(.6) + 0.0(.4)] /1.07 = 18.93

• Intrinsic value is 114.49 - 100 = 14.49. Do not Intrinsic value is 114.49 - 100 = 14.49. Do not exercise early. European call would be worth 17.69.exercise early. European call would be worth 17.69.


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Trading Strategies for Options on Futures

Buy a Call Option on FuturesBuy a Call Option on Futures Profit equation: Profit equation: = Max(0,fT - X) - C

= f= fTT - X - C if f - X - C if fTT X

= - C if f= - C if fTT X

See Figure 12.6, p. 525 for December 110 T-bond futures call, C = $1.234375.


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Trading Strategies for Options on Futures (continued)

Buy a Put Option on FuturesBuy a Put Option on Futures Profit equation: Profit equation: = Max(0,X - fT) - P

= - P if f= - P if fTT X

= X - f= X - fTT - P if f - P if fTT X

See Figure 12.7, p. 526 for December 110 T-bond futures put, P = $2.515625.


16

Trading Strategies for Options on Futures (continued)

Write a Covered Call Option on FuturesWrite a Covered Call Option on Futures Profit equation: Profit equation: = fT - f0 - Max(0,fT - X) + C

= X - f= X - f00 + C if f + C if fTT X

= f= fTT - f - f00 + C if f + C if fTT X

See Figure 12.8, p. 528 for December 110 T-bond futures covered call, C = $1.234375, f = 108.71875.


17

Options on Futures Versus Options on the Spot

With no dividends futures price is always higher than spot With no dividends futures price is always higher than spot price prior to expiration.price prior to expiration.

So call option on futures is on a higher priced instrument So call option on futures is on a higher priced instrument than call option on spot, butthan call option on spot, but This applies to American calls only because European This applies to American calls only because European

calls cannot be exercised until expiration.calls cannot be exercised until expiration. Similar line of reasoning applies to puts on futures.Similar line of reasoning applies to puts on futures. Futures options are the only exchange-listed options that Futures options are the only exchange-listed options that

trade side-by-side with the underlying instrument.trade side-by-side with the underlying instrument. Easier to transact in the underlying when it is a futures than Easier to transact in the underlying when it is a futures than

when it is a stock index.when it is a stock index.


18

Summary

See See Figure 12.9, p. 531Figure 12.9, p. 531..

Appendix 12. Selected Options on Futures Contract Specifications

Documents

Copyright © 2001 by Harcourt, Inc. All rights reserved.1 Chapter 12: Options on Futures My option gave me the right to a futures contract for that much