36 lines
2.7 KiB
Plaintext
36 lines
2.7 KiB
Plaintext
798 Part VI: Measuring and Trading Volatility
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model, for example, uses a lognormal distribution. Personally, this author believes
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that the Black-Scholes model is an excellent tool for analyzing options and option
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strategies, but one must understand that it may not be affording enough probability
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to large moves by the underlying.
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Does this mean that most options are underpriced, since traders and market
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makers are using the Black-Scholes model (or similar models) to price them?
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Without getting too technical, the answer is that yes, some options - particularly out
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of-the-money options - are probably underpriced. However, one must understand
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that it is still a relatively rare occurrence to experience one of these big moves - ifs
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just not as rare as the lognormal distribution would indicate. So, an out-of-the-money
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option might be slightly underpriced, but often not enough to make any real differ
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ence.
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In fact, futures options in grains, gold, oil, and other markets that often experi
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ence large and sudden rallies display a distinct volatility skew. That is, out-of-the-money
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call options trade at significantly higher implied volatilities than do at-the-money
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options. Ironically, there is far less chance of one of these hyper-standard-deviation
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moves occurring in commodities than there is in stocks, at least if history is a guide. So,
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the fact that some out-of-the-money futures options are expensive is probably an incor
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rect overadjustment for the possibility of large moves.
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THE PROBABILITY OF STOCK PRICE MOVEMENT
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The distribution information introduced in this chapter can be incorporated into
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somewhat rigorous methods of determining probabilities. That is, one can attempt to
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assess the chances of a stock, futures contract, or index moving by a given distance,
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and those chances can incorporate the fat tails or other non-lognormal behavior of
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prices.
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The software that calculates such probabilities is typically named a "probability
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calculator." There are many such software programs available in the marketplace.
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They range from free calculators to completely overpriced ones selling for more than
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$1,000. In reality, high-level probability calculation software can be created by some
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one with a good understanding of statistics, or a program can be purchased for a
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rather nominal fee - perhaps $100 or so.
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Before getting into these various methods of probability estimation, it should be
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noted that all of them require the trader to input a volatility estimate. There are only
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a few other inputs, usually the stock price, target price(s), and length of time of the
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study. The volatility one inputs is, of course, an estimate of future volatility - some- |