35 lines
2.1 KiB
Plaintext
35 lines
2.1 KiB
Plaintext
Chapter 40: Advanced Concepts 903
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Recall that this is the sixth risk measurement of an option position. The gamma
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of the gamma is the anwunt by which the gamma will change when the stock price
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changes.
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Recall that in the earlier discussion of gamma, it was noted that gamma
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changes. This example is based on the same example used earlier.
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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 1 point to 50, the delta of the call will increase by
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the amount of the gamma: It will increase from 0.50 to 0.55. Simplistically, if XYZ
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moves up another point to 51, the delta will increase by another 0.05, 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.
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In reality, the gamma decreases as the stock moves away from the strike. Thus,
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with XYZ at 51, the gamma might only be 0.04. Therefore, if XYZ moved up to 52,
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the call's delta would only increase by 0.04, to 0.64. Hence, the gamma of the gamma
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is -0.01, since the gamma decreased from .05 to .04 when the stock rose by one
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point.
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As XYZ moves higher and higher, the gamma will get smaller and smaller.
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Eventually, with XYZ in the low 60's, the delta will be nearly 1.00 and the gamma
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nearly 0.00.
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This change in the gamma as the stock moves is called the gamma of the
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gamma. It is probably referred to by other names, but since its use is limited to only
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the most sophisticated traders, there is no standard name. Generally, one would use
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this measure on his entire portfolio to gauge how quickly the portfolio would be
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responding to the position gamma.
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Example: With XYZ at 31. 75 as in some of the previous examples, the following risk
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measures exist:
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Option Option Option Position
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Position Delta Gamma Gamma/Gamma Gamma/Gamma
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Short 4,500 XYZ 1.00 0.00 0.0000 0
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Short 100 XYZ April 25 calls 0.89 0.01 -0.0015 -15
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Long 50 XYZ April 30 calls 0.76 0.03 -0.0006 - 3
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Long 139 XYZ July 30 calls 0.74 0.02 -0.0003 - 4
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Total Gamma of Gamma: -22 |