24 lines
1.5 KiB
Plaintext
24 lines
1.5 KiB
Plaintext
a faster rate and lose value at a slower rate, (positive) gamma helps the
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option buyer. A trader buying one call or put in these examples would have
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+0.04 gamma. Buying 10 of these options would give the trader a +0.4
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gamma.
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When traders sell options, gamma works against them. When options lose
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value, they move toward zero at a slower rate. When the underlying moves
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adversely, gamma speeds up losses. Selling options yields a negative
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gamma position. A trader selling one of the above calls or puts would have
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−0.04 gamma per option.
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The effect of gamma is less significant for small moves in the underlying
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than it is for bigger moves. On proportionately large moves, the delta can
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change quite a bit, making a big difference in the position’s P&(L). In
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Exhibit 2.1 , the left side of the diagram showed the call price not
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increasing at all with advances in the stock—a 0 delta. The right side
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showed the option advancing in price 1-to-1 with the stock—a 1.00 delta.
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Between the two extremes, the delta changes. From this diagram another
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definition for gamma can be inferred: gamma is the second derivative of the
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graph of the option price relative to the stock price. Put another way,
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gamma is the first derivative of a graph of the delta relative to the stock
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price. Exhibit 2.5 illustrates the delta of a call relative to the stock price.
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EXHIBIT 2.5 Call delta compared with stock price.
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Not only does the delta change, but it changes at a changing rate. Gamma
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is not constant. Moneyness, time to expiration, and volatility each have an
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effect on the gamma of an option. |