36 lines
2.7 KiB
Plaintext
36 lines
2.7 KiB
Plaintext
Chapter 38: The Distribution of Stock Prices 797
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models predict; but it certainly means that the buyer of underpriced options stands
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to benefit in a couple of ways. Conversely, an option seller must certainly concentrate
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his efforts where options are expensive, and even then should be acutely aware that
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he may experience larger-than-expected stock price movements while the option
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position is in place.
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So what does this mean for option strategies? On the surface, it means that if
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one uses the normal (or lognormal) distribution for estimating the probability of a
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strategy's success, he may get a big move in the stock that he didn't originally view as
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possible. If one were long straddles, that's great. However, if he is short naked
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options, then there could be a nasty surprise in store. That's one reason why extreme
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caution should be used regarding selling naked options on stocks; they can make
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moves of this sort too often. At least with indices, such moves are far less frequent,
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although the Dow drop of over 550 points in October 1997 was a move of seven stan
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dard deviations, and the crash of '87 was about a 16-standard deviation move - which
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Professor Mark Rubenstein of the University of California at Berkeley says was some
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thing that should occur about once in ten times the life of our current universe! That's
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according to lognormal distribution, of course, which we know understates things
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somewhat, but it's still a big number under any distribution.
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There are two approaches that one can take, then, regarding option strategies.
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One is to invent another method for estimating stock price distributions. Suffice it to
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say that that is not an easy task, or someone would have made it well-known already.
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There have been many attempts, including some in which a large history of stock
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price movements is observed and then a distribution is fitted to them. The problem
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with accounting for these occasional large price moves is that it is perhaps an even
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more grievous error to overestimate the probabilities of such moves than to underes
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timate them.
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The second approach is to continue to use the normal distribution, because it's
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fast and accessible in a lot of places. Then, either rely on option buying strategies
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( straddles, for example) where implied volatility appears to be low - knowing that you
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have a chance at better results than the statistics might indicate - or adjust your cal
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culations mentally for these large potential movements if you are using option selling
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strategies.
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THE PRICING OF OPTIONS
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The extreme movements of the fat tail distribution should be figured into the pricing
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of an option, but they really are not, at least not by most models. The Black-Scholes |