38 lines
2.9 KiB
Plaintext
38 lines
2.9 KiB
Plaintext
808 Part VI: Measuring and Trading Volatility
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of them resulted in the stock being unchanged. Also, only about 2,500 or them, or
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1110th of one percent, resulted in a move of-4.0 standard deviations or more. Those
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percentages, along with all of the others, would be built into the computer, so that
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the total distribution accounts for 100% of all possible stock movements.
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Then, we tell the computer to allow a stock to move randomly in accordance
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with whatever volatility the user has input. So, there would be a fairly large proba
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bility that it wouldn't move very far on a given day, and a very small probability that
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it would move three or more standard deviations. Of course, with the fat tail distri
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bution, there would be a larger probability of a movement of three or more standard
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deviations than there would be with the regular lognormal distribution. The Monte
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Carlo simulation progresses through the given number of trading days, moving the
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stock cumulatively as time passes. If the stock hits the break-even price, that partic
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ular simulation can be terminated and the next one begun. At the end of all the tri
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als (100,000 perhaps), the number in which the upside target was touched is divided
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by the total number of trials to give the probability estimate.
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Is it really worth all this extra trouble to evaluate these more complicated prob
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ability distributions? It seems so. Consider the following example:
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Example: Suppose that a trader is considering selling naked puts on XYZ stock,
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which is currently trading at a price of 80. He wants to sell the November 60 puts,
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which expire in two months. Although XYZ is a fairly volatile stock, he feels that he
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wouldn't mind owning it if it were put to him. However, he would like to see the puts
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expire worthless. Suppose the following information is available to him via the vari
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ous probability calculators:
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Simple "end point" probability of XYZ < 60 at expiration: 10%
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Probability that XYZ ever trades < 60 (using the lognormal distribution) 20%
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Probability that XYZ ever trades < 60 (using the fat tail distribution): 22%
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If the chances of the put never needing attention were truly only 10%, this trader
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would probably sell the puts naked and feel quite comfortable that he had a trade
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that he wouldn't have to worry too much about later on. However, if the true proba
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bility that the put will need attention is 22%, then he might not take the trade. Many
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naked option sellers try to sell options that have only probabilities of 15% or less of
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potentially becoming troublesome.
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Hence, the choice of which probability calculation he uses can make a differ
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ence in whether or not a trade is established.
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Other strategies lend themselves quite well to probability analysis as well.
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Credit spreaders - sellers of out-of-the-money put spreads - usually attempt to quan
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tify the probability of having to take defensive action. Any action to adjust or remove |