37 lines
2.4 KiB
Plaintext
37 lines
2.4 KiB
Plaintext
904 Part VI: Measuring and Trading Volatility
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Recall that, in the same example used to describe gamma, the position was delta
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long 686 shares and had a positive gamma of 328 shares. Furthermore, we now see
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that the gamma itself is going to decrease as the stock moves up ( it is negative) or will
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increase as the stock moves down. In fact, it is expected to increase or decrease by
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22 shares for each point XYZ moves.
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So, if XYZ moves up by 1 point, the following should happen:
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a. Delta increases from 686 to 1,014, increasing by the amount of the gamma.
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b. Gamma decreases from 328 to 306, indicating that a further upward move by
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XYZ will result in a smaller increase in delta.
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One can build a general picture of how the gamma of the gamma changes over
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different situations - in- or out-of-the-money, or with more or less time remaining
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until expiration. The following table of two index calls, the January 350 with one
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month of life remaining and the December 350 with eleven months of life remain
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ing, shows the delta, gamma, and gamma of the gamma for various stock prices.
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Index January 350 call December 350 call
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Price Delta Gamma Gamma/Gamma Delta Gamma Gamma/Gamma
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310 .0006 .0001 .0000 .3203 .0083 .0000
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320 .0087 .0020 .0004 .3971 .0082 .0000
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330 .0618 .0100 .0013 .4787 .0080 -.0000
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340 .2333 .0744 .0013 .5626 .0078 -.0001
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350 .5241 .0309 -.0003 .6360 .0073 -.0001
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360 .7957 .0215 -.0014 .6984 .0067 -.0001
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370 .9420 .0086 -.0010 .7653 .0060 -.0001
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380 .9892 .0021 -.0003 .8213 .0052 -.0001
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Several conclusions can be drawn, not all of which are obvious at first glance.
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First of all, the gamma of the gamma for long-term options is very small. This should
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be expected, since the delta of a long-term option changes very slowly. The next fact
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can best be observed while looking at the shorter-term January 350 table. The
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gamma of the gamma is near zero for deeply out-of-the-money options. But, as the
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option comes closer to being in-the-money, the gamma of the gamma becomes a pos
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itive number, reaching its maximum while the option is still out-of-the-money. By the
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time the option is at-the-money, the gamma of the gamma has turned negative. It
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then remains negative, reaching its most negative point when slightly in-the-money.
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From there on, as the option goes even deeper into-the-money, the gamma of the
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gamma remains negative but gets closer and closer to zero, eventually reaching
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(minus) zero when the option is very far in-the-money. |