Add training workflow, datasets, and runbook
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Chapter 33: Mathematical Considerations for Index Products 64S
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idend is subtracted from the index price and the model is evaluated using that adjust
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ed stock price. With stock options, there was a second alternative - shortening the
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time to expiration to be equal to the ex-date - but that is not viable with index options
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since there are numerous ex-dates.
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Let's look at an example using the same fictional dividend information and index
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that were used in Chapter 30 on stock index hedging strategies.
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Example: Assume that we have a capitalization-weighted index composed of three
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stocks: AAA, BBB, and CCC. The following table gives the pertinent information
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regarding the dividends and floats of these three stocks:
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Dividend Days until
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Stock Amount Dividend Float
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AAA 1.00 35 50,000,000
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BBB 0.25 60 35,000,000
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CCC 0.60 8 120,000,000
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Divisor: 150,000,000
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One first computes the present worth of each stock's dividend, multiplies that
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amount by the float, and then divides by the index divisor. The sum of these compu
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tations for each stock gives the total dividend for the index. The present worth of the
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dividend for this index is $0.8667.
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Assume that the index is currently trading at 175.63 and that we want to evalu
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ate the theoretical value of the July 175 call. Then, using the Black-Scholes model,
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we would perform the following calculations:
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1. Subtract the present worth of the dividend, 0.8667, from the current index price
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of 175.63, giving an adjusted index price of 174.7633.
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2. Evaluate the call's fair value using 17 4. 7633 as the stock price. All other variables
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are as they are for stocks, including the risk-free interest rate at its actual value
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(10%, for example).
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The theoretical value for puts is computed in the same way as for equity
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options, by using the arbitrage model. This is sufficient for cash-based index options
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because it is possible - albeit difficult to hedge these options by buying or selling
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the entire index. Thus, the options should reflect the potential for such arbitrage.
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The put value should, of course, reflect the potential for dividend arbitrage with the
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index. The arbitrage valuation model p"resented in Chapter 28 on modeling called for
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the dividend to be used. For these index puts, one would use the present worth of
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