35 lines
2.2 KiB
Plaintext
35 lines
2.2 KiB
Plaintext
646 Part V: Index Options and Futures
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the dividend on the index - the same one that was used for the call valuation, as in
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the last example.
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THE IMPLIED DIVIDEND
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If one does not have access to all of the dividend information necessary to make the
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"present worth of the dividends" calculation (i.e., if he is a private individual or pub
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lic customer who does not subscribe to a computer-based dividend "service"), there
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is still a way to estimate the present worth of the dividend. All one need do is make
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the assumption that the market- makers know what the present worth of the dividend
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is, and are thus pricing the options accordingly. The individual public customer can
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use this information to deduce what the dividend is.
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Example: OEX is trading at 700, the June options have 30 days of life remaining, the
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short-term interest rate is 10%, and the following prices exist:
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June 700 call: 18.00
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June 700 put: 14.50
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One can use iterations of the Black-Scholes model to determine what the OEX
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"dividend" is. In this case, it turns out to be something on the order of $2.10.
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Briefly, these are the steps that one would need to follow in order to determine
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this dividend:
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1. Assume the dividend is $0.00.
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2. Using the assumed dividend, use the Black-Scholes model to determine the
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implied volatility of the call option, whose price is known (18.00 in the above
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example).
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3. Using the implied volatility determined from step 2 and the assumed dividend,
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is the arbitrage put value as derived from the Black-Scholes calculations at the
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end of step 2 roughly equal to the market value of the put (14.50 in the above
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example)? If yes, you are done. If not, increase the assumed dividend by some
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nominal amount, say $0.10, and return to step 2.
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Thus, without having access to complete dividend information, one can use the
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information provided to him by the marketplace in order to imply the dividend of an
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index option. The only assumption one makes is that the market-makers know what
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the dividend is (they most assuredly do). Note that the implied volatility of the
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options is determined concurrently with the implied dividend (step 2 above). A veiy
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useful tool, this simple "implied dividend calculator" can be added to any software
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that employs the Black-Scholes model. |