37 lines
2.8 KiB
Plaintext
37 lines
2.8 KiB
Plaintext
Chapter 40: Advanced Concepts 905
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Can one possibly reason this risk measurement out without making severe
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mathematical calculations? Well, possibly. Note that the delta of an option starts as a
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small number when the option is out-of-the-money. It then increases, slowly at first,
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then more quickly, until it is just below 0.60 for an at-the-money option. From there
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on, it will continue to increase, but much more slowly as the option becomes in-the
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money. This movement of the delta can be observed by looking at gamma: It is the
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change in the delta, so it starts slowly, increases as the stock nears the strike, and then
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begins to decrease as the option is in-the-money, always remaining a positive num
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ber, since delta can only change in the positive direction as the stock rises. Finally,
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the gamma of the gamma is the change in the gamma, so it in tum starts as a positive
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number as gamma grows larger; but then when gamma starts tapering off, this is
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reflected as a negative gamma of the gamma.
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In general, the gamma of the gamma is used by sophisticated traders on large
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option positions where it is not obvious what is going to happen to the gamma as the
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stock changes in price. Traders often have some feel for their delta. They may even
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have some feel for how that delta is going to change as the stock moves (i.e., they
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have a feel for gamma). However, sophisticated traders know that even positions that
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start out with zero delta and zero gamma may eventually acquire some delta. The
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gamma of the gamma tells the trader how much and how soon that eventual delta will
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be acquired.
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MEASURING THE DIFFERENCE OF IMPLIED VOLATILITIES
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Recall that when the topic of implied volatility was discussed, it was shown that if one
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could identify situations in which the various options on the same underlying securi
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ty had substantially different implied volatilities, then there might be an attractive
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neutral spread available. The strategist might ask how he is to determine if the dis
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crepancies between the individual options are significantly large to warrant attention.
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Furthermore, is there a quick way (using a computer, of course) to determine this?
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A logical way to approach this is to look at each individual implied volatility and
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compute the standard deviation of these numbers. This standard deviation can be
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converted to a percentage by dividing it by the overall implied volatility of the stock.
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This percentage, if it is large enough, alerts the strategist that there may be opportu
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nities to spread the options of this underlying security against each other. An exam
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ple should clarify this procedure.
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Example: XYZ is trading at 50, and the following options exist with the indicated
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implied volatilities. We can calculate a standard deviation of these implieds, called
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implied deviation, via the formula: |