36 lines
2.3 KiB
Plaintext
36 lines
2.3 KiB
Plaintext
Chapter 40: Advanced Concepts 855
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to nearly 1.00 because of the short time remaining until expiration. Thus, the gamma
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would be roughly 0.25 (the delta increased by 0.50 when the stock moved 2 points),
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as compared to much smaller values of gamma for at-the-money options with several
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weeks or months of life remaining. The same 2-point rise in the underlying stock
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would not result in much of an increase in the delta of longer-term options at all.
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Out-of-the-money options display a different relationship between gamma and
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time remaining. An out-of-the-money option that is about to expire has a very small
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delta, and hence a very small gamma. However, if the out-of-the-money option has a
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significant amount of time remaining, then it will have a larger gamma than the
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option that is close to expiration.
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Figure 40-4 (see Table 40-4) depicts the gammas of three options with varying
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amounts of time remaining until expiration. The properties regarding the relation
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ship of gamma and time can be observed here. Notice that the short-term options
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have very low gammas deeply in- or out-of the-money, but have the highest gamma
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at-the-money (at 50). Conversely, the longest-term, one-year option has the highest
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gamma of the three time periods for deeply in- or out-of-the-money options. The
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data is presented in Table 40-4. This table contains a slight amount of additional data:
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the gamma for the at-the-money option at even shorter periods of time remaining
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until expiration. Notice how the gamma explodes as time decreases, for the at-the
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money option. With only one week remaining, the gamma is over 0.28, meaning that
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the delta of such a call would, for example, jump from 0.50 to 0.78 if the stock mere
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ly moved up from 50 to 51.
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Gamma is dependent on the volatility of the underlying security as well. At-the
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money options on less volatile securities will have higher gammas than similar options
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on more volatile securities. The following example demonstrates this fact.
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Example: Assume XYZ is at 49, as is ABC. Moreover, XYZ is a more volatile stock
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(30% implied) as compared to ABC (20% ). Then, similar options on the two stocks
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would have significantly different gammas.
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XYZ Gammas ABC Gammas
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Option (Volatility = 30%) (Volatility= 20%)
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January 50 .066 .097
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January 55 .045 .039
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January 60 .019 .0053
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February 50 .055 .081
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February 60 .024 .011 |