35 lines
2.6 KiB
Plaintext
35 lines
2.6 KiB
Plaintext
854 Part VI: Measuring and Trading Volatility
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Example: With XYZ at 49, assume the January 50 call has a delta of 0.50 and a
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gamma of 0.05. If XYZ moves up one point to 50, the delta of the call will increase
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by the amount of the gamma: It will increase from 0.50 to 0.55.
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As with the delta, the gamma can also be expressed as a percentage. But in this
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case, the increase or decrease applies to the delta.
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Example: Again, with XYZ at 49, assume the January 50 call has a delta of 0.50 and a
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gamma of 0.05. If XYZ moves up 2 points to 51, the delta of the call will increase by
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5% of the stock rrwve, because the gamma is 0.05, or 5 percent. Five percent of the
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stock move is 0.05 x 2, or 0.10. Thus, the delta will increase by 0.10, from 0.50 to 0.60.
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Obviously, the delta cannot keep increasing by 0.05 each time XYZ gains anoth
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er point in price, for it will eventually exceed 1.00 by that calculation, and it is known
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that the delta has a maximum of 1.00. Thus, it is obvious that the gamma changes. In
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general, the gamma is at its maximum point when the stock is near the strike of the
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option. As the stock moves away from the strike in either direction, the gamma
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decreases, approaching its minimum value of zero.
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Conceptually, this means that a deeply in-the-money or deeply out-of-the
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money option has a gamma of nearly zero. This makes sense - it implies that the delta
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of a deep in- or deep out-of-the-money option does not change very much at all, even
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if the stock moves by one point.
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Example: Assume XYZ is 25, and the January 50 call has a delta of virtually zero. If
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XYZ moves up one point to 26, the call is still so far out-of-the-money that the delta
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will still be zero. Thus, the gamma of this call is zero, since the delta does not change
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when the stock increases in price by a point.
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In a similar manner, the January 45 put on XYZ would have a delta of -1.0 with
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XYZ at 25. If XYZ moved up one point to 26, the put' s delta would not change; it is
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still so far in-the-money that it would still be - 1.0. Thus, the gamma of this deeply
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in-the-money option is also zero, since the delta remains unchanged in the face of a
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I-point rise in the underlying security.
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Note that the gamma of any option is expressed as a positive number, whether
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the option is a put or a call.
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Other properties of gamma are useful to know as well. As expiration nears, the
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gamma of at-the-money options increases dramatically. Consider an option with a day
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or two of life remaining. If it is at-the-money, the delta is approximately 0.50.
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However, if the stock were to move 2 points higher, the delta of the option would jump |