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1、Chapter 17 Futures OptionsOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20121Options on FuturesReferred to by the maturity month of the underlying futures The option is American and usually expires on or a few days before the earliest delivery date of the underlying fu
2、tures contractOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20122Mechanics of Call Futures OptionsWhen a call futures option is exercised the holder acquires A long position in the futures A cash amount equal to the excess of the futures price at the time of the most r
3、ecent settlement over the strike price Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20123Mechanics of Put Futures OptionWhen a put futures option is exercised the holder acquires A short position in the futures A cash amount equal to the excess of the strike price ove
4、r the futures price at the time of the most recent settlementOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20124Example 1 (page 361)Dec. call option contract on copper futures has a strike of 240 cents per pound. It is exercised when futures price is 251 cents and most
5、 recent settlement is 250. One contract is on 250,000 pounds Trader receives Long Dec. futures contract on copper $2,500 in cashOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20125Example 2 (page 362)Dec put option contract on corn futures has a strike price of 400 cent
6、s per bushel. It is exercised when the futures price is 380 cents per bushel and the most recent settlement price is 379 cents per bushel. One contract is on 5000 bushels Trader receives Short Dec futures contract on corn $1,050 in cashOptions, Futures, and Other Derivatives, 8th Edition, Copyright
7、John C. Hull 20126The PayoffsIf the futures position is closed out immediately: Payoff from call = F K Payoff from put = K F where F is futures price at time of exerciseOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20127Potential Advantages of Futures Options over Spot
8、 OptionsFutures contracts may be easier to trade and more liquid than the underlying asset Exercise of option does not lead to delivery of underlying asset Futures options and futures usually trade on same exchange Futures options may entail lower transactions costsOptions, Futures, and Other Deriva
9、tives, 8th Edition, Copyright John C. Hull 20128European Futures OptionsEuropean futures options and spot options are equivalent when futures contract matures at the same time as the optionIt is common to regard European spot options as European futures options when they are valued in the over-the-c
10、ounter marketsOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 20129Put-Call Parity for Futures Options (Equation 16.1, page 345)Consider the following two portfolios: 1. European call plus KerT of cash2. European put plus long futures plus cash equal to F0erT They must b
11、e worth the same at time T so that c + KerT = p + F0erTOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201210Other RelationsF0 erT K (F0 K)erTp (F0 K)erTOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201211Binomial Tree ExampleA 1-month call
12、 option on futures has a strike price of 29. Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201212Futures Price = $28 Option Price = $0Futures Price = $33 Option Price = $4Futures Price = $30 Option Price = ?Setting Up a Riskless PortfolioConsider the Portfolio:long D f
13、utures short 1 call optionPortfolio is riskless when 3D 4 = 2D or D = 0.8Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 2012133D 42DValuing the Portfolio ( Risk-Free Rate is 6% )The riskless portfolio is: long 0.8 futures short 1 call option The value of the portfolio i
14、n 1 month is 1.6 The value of the portfolio today is 1.6e0.06/12 = 1.592Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201214Valuing the OptionThe portfolio that is long 0.8 futures short 1 optionis worth 1.592 The value of the futures is zero The value of the option mu
15、st therefore be 1.592Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201215Generalization of Binomial Tree Example (Figure 17.2, page 368)A derivative lasts for time T and is dependent on a futures priceOptions, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201216F0uuF0ddF0Generalization (continued)Consider the portfolio that is long D futures and short 1 derivativeThe portfolio is riskless when Options, Futures, and Other Derivatives, 8th Edition, Copyright John C. Hull 201217F0u D - F0 D uF0d D- F0D dGeneralization (continued)Value of the p
