34 lines
2.5 KiB
Plaintext
34 lines
2.5 KiB
Plaintext
644 Part V: Index Options and Futures
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These same strategies apply to options on futures. However, boxes on cash
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based options involve another consideration. It is often the case with cash-based
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options that the box sells for more than the difference in the strikes. For example, a
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box in which the strikes are 10 points apart might sell for 10.50, a substantial premi
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um over the striking price differential. The reason that this happens is because of the
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possibility of early assignment. The seller of the box assumes that risk and, as a result,
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demands a higher price for the box.
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If he sells the box for half a point more than the striking price differential, then
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he has a built-in cushion of .50 point of index movement if he were to be assigned
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early. In general, box strategies are not particularly attractive. However, if the pre
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mium being paid for the box is excessively high, then one should consider selling the
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box. Since there are four commissions involved, this is not normally a retail strategy.
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MATHEMATICAL APPLICATIONS
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The following material is intended to be a companion to Chapter 28 on mathemati
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cal applications. Index options have a few unique properties that must be taken into
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account when trying to predict their value via a model.
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The Black-Scholes model is still the model of choice for options, even for index
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options. Other models have been designed, but the Black-Scholes model seems to
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give accurate results without the extreme complications of most of the other models.
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FUTURES
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Modeling the fair value of most futures contracts is a difficult task. The
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Black-Scholes model is not usable for that task. Recall that we saw earlier that the
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fair value of a future contract on an index could be calculated by computing the pres
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ent value of the dividend and also knowing the savings in carrying cost of the futures
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contract versus buying the actual stocks in the index.
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CASH-BASED INDEX OPTIONS
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The futures fair value model for a capitalization-weighted index requires knowing the
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exact dividend, dividend payment date, and capitalization of each stock in the index
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(for price-weighted indices, the capitalization is unnecessary). This is the only way of
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getting the accurate dividend for use in the model. The same dividend calculation
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must be done for any other index before the Black-Scholes formula can be applied.
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In the actual model, the dividend for cash-based index options is used in much
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the same way that dividends are used for stock options: The present value of the div- |