35 lines
2.2 KiB
Plaintext
35 lines
2.2 KiB
Plaintext
Chapter 34: Futures and Futures Options 677
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Thus, if one is long 8 calls with a delta of 0. 75, then that position has an EFP of
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6 (8 x 0.75). This means that being long those 8 calls is the same as being long 6
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futures contracts.
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Note that in the case of stocks, the equivalent stock position formula has anoth
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er factor shares per option. That concept does not apply to futures options, since
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they are always options on one futures contract.
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MATHEMATICAL CONSIDERATIONS
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This brief section discusses modeling considerations for futures options and options
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on physicals.
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Futures Options. The Black model (see Chapter 33 on mathematical consider
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ations for index options) is used to price futures options. Recall that futures don't pay
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dividends, so there is no dividend adjustment necessary for the model. In addition,
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there is no carrying cost involved with futures, so the only adjustment that one needs
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to make is to use 0% as the interest rate input to the Black-Scholes model. This is an
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oversimplification, especially for deeply in-the-money options. One is tying up some
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money in order to buy an option. Hence, the Black model will discount the price
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from the Black-Scholes model price. Therefore, the actual pricing model to be used
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for theoretical evaluation of futures options is the Black model, which is merely the
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Black-Scholes model, using 0% as the interest rate, and then discounted:
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Call Theoretical Price = e-rt x Black-Scholes formula [r = O]
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Recall that it was stated above that:
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Futures call = Futures put + Future price - Strike price
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The actual relationship is: ~
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Futures call= Futures put+ e-rt (Futures price - Strike price)
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where
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r = the short-term interest rate,
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t = the time to expiration in years, and
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e-rt = the discounting factor.
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The short-term interest rate has to be used here because when one pays a debit
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for an option, he is theoretically losing the interest that he could earn if he had that
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money in the bank instead, earning money at the short-term interest rate.
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The difference between these two formulae is so small for nearby options that
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are not deeply in-the-money that it is normally less than the bid-asked spread in the
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options, and the first equation can be used. |