37 lines
2.9 KiB
Plaintext
37 lines
2.9 KiB
Plaintext
Chapter 36: The Basics of Volatility Trading 731
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probability models. We need to be able to make volatility estimates in order to deter
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mine whether or not a strategy might be successful, and to determine whether the
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current option price is a relatively cheap one or a relatively expensive one. For exam
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ple, one can't just say, "I think XYZ is going to rise at least 18 points by February expi
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ration." There needs to be some basis in fact for such a statement and, lacking inside
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information about what the company might announce between now and February,
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that basis should be statistics in the form of volatility projections.
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Historical volatility is, of course, useful as an input to the (Black-Scholes) option
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model. In fact, the volatility input to any model is crucial because the volatility com
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ponent is such a major factor in determining the price of an option. Furthermore,
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historical volatility is useful for more than just estimating option prices. It is neces
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sary for making stock price projections and calculating distributions, too, as will be
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shown when those topics are discussed later. Any time one asks the question, "What
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is the probability of the stock moving from here to there, or of exceeding a particu
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lar target price?" the answer is heavily dependent on the volatility of the underlying
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stock (or index or futures).
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It is obvious from the above example that historical volatility can change dra
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matically for any particular instrument. Even if one were to stick with just one
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measure of historical volatility ( the 20-day historical is commonly the most popular
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measure), it changes with great frequency. Thus, one can never be certain that bas
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ing option price predictions or stock price distributions on the current historical
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volatility will yield the "correct" results. Statistical volatility may change as time
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goes forward, in which case your projections would be incorrect. Thus, it is impor
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tant to make projections that are on the conservative side.
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ANOTHER APPROACH: GARCH
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GARCH stands for Generalized Autoregressive Conditional Heteroskedasticity,
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which is why it's shortened to GARCH. It is a technique for forecasting volatility that
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some analysts say produces better projections than using historical volatility alone or
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implied volatility alone. GARCH was created in the 1980s by specialists in the field of
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econometrics. It incorporates both historical and implied volatility, plus one can throw
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in a constant ("fudge factor"). In essence, though, the user of GARCH volatility mod
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els has to make some predictions or decisions about the weighting of the factors used
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for the estimate. By its very nature, then, it can be just as vague as the situations
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described in the previous section.
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The model can "learn," though, if applied correctly. That is, if one makes a
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volatility prediction for today (using GARCH, let's say), but it turns out that the actu- |