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Futures Options Chapter

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16.2 The Goals of Chapter 16 Introduce mechanics of futures options Properties of futures options Pricing futures options using binomial trees Pricing futures options with Black’s formula Introduce futures-style options

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Mechanics of Futures Options

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Mechanics of Futures Options 16.4

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Mechanics of Futures Options 16.5

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Futures Options vs. Spot Options 16.6 Advantages of futures options –Futures contracts may be more convenient to trade than underlying assets 1000 barrels of oil vs. one oil futures contract –Futures prices are more readily available Treasury bonds in dealers markets vs. Treasury bond futures on exchanges –The liquidity of futures contract is in general better than underlying assets This is because the leverage effect of the margin mechanism or that many speculators intend to bid the direction of the price movement but do not want to hold the underlying assets physically

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Futures Options vs. Spot Options 16.7 –Exercise of the futures option does not lead to the delivery of the underlying asset The futures contracts are usually closed out before maturity and thus settled in cash –Futures options and futures usually trade in pits side by side on the same exchanges In most cases, if an exchange offers a futures contract, it also offers the corresponding futures option contract This arrangement can facilitates the needs of hedging, arbitrage, and speculation and in effect enhance the overall trading volume –Futures options may entail lower transactions costs than spot options in many situations

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16.8 Futures Options vs. Spot Options

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16.9 Futures Options vs. Spot Options

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Properties of Futures Options

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Properties of Futures Options Portfolio A Call futures option Cash Total Portfolio B Put futures option Long futures Cash Total

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Properties of Futures Options 16.12

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Properties of Futures Options Futures optionsSpot options Lower bound for European calls Lower bound for European puts Upper bound for European calls Upper bound for European puts Lower bound for American calls Lower bound for American puts Upper bound for American calls Upper bound for American puts Put-call parity for American options

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Pricing Futures Options with Binomial Tree Model

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Binomial Tree for Futures Options One-period binomial tree model for futures options –A 1-month call option on futures has a strike price of 29 –The current futures price is 30 and it will move either upward to 33 or downward to 28 over 1 month

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– 4 –2 Binomial Tree for Futures Options

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16.17 Binomial Tree for Futures Options

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16.18

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16.19 Binomial Tree for Futures Options

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16.20 Binomial Tree for Futures Options

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16.21 Binomial Tree for Futures Options

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16.22 Binomial Tree for Futures Options

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Growth Rates For Futures Prices 16.23

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Growth Rates For Futures Prices –Consequently, the expected growth rate of the futures price is therefore zero –The futures price can therefore be treated like a stock paying a dividend yield of r –This is consistent with the results we have presented so far (put-call parity, bounds, binomial trees) –Based on the same reasoning, we can modifying the Black-Scholes formula to price futures options shown in the next section 16.24

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Summary of Key Results from Chapters 15 and

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Pricing Futures Options with Black’s Model

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16.27 Black’s Model for Pricing Futures Options

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Black’s Model for Pricing Spot Options 16.29

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16.30 Black’s Model for Pricing Spot Options

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16.31 Black’s Model for Pricing Spot Options

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Futures-Style Options

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Futures-Style Options A futures-style option is a futures contract on the option payoff –Note that to trade either spot or futures options, traders should pay (receive) cash up front –In contrast, traders who trade a futures-style option post margin in the same way that they do on a regular futures contract –The contract is settled daily to reflect the current option value and the final settlement price is the payoff (or equivalently the final value) of the option –Due to the attraction of the leverage effect, some exchanges trade futures-style options in preference to regular futures options 16.33

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Futures-Style Options 16.34

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