22 lines
1.3 KiB
Plaintext
22 lines
1.3 KiB
Plaintext
Dynamic Gamma
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When options are far in-the-money or out-of-the-money, they are either
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1.00 delta or 0 delta. At the extremes, small changes in the stock price will
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not cause the delta to change much. When an option is at-the-money, it’s a
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different story. Its delta can change very quickly.
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ITM and OTM options have a low gamma.
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ATM options have a relatively high gamma.
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Exhibit 2.6 is an example of how moneyness translates into gamma on
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QQQ calls.
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EXHIBIT 2.6 Gamma of QQQ calls with QQQ at $44.
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With QQQ at $44, 92 days until expiration, and a constant volatility input
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of 19 percent, the 36- and 54-strike calls are far enough in- and out-of-the-
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money, respectively, that if the Qs move a small amount in either direction
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from the current price of $44, the movement won’t change their deltas
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much at all. The chances of their money status changing between now and
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expiration would not be significantly different statistically given a small
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stock price change. They have the smallest gammas in the table.
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The highest gammas shown here are around the ATM strike prices. (Note
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that because of factors not yet discussed, the strike that is exactly at-the-
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money may not have the highest gamma. The highest gamma is likely to
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occur at a slightly higher strike price.) Exhibit 2.7 shows a graph of the
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corresponding numbers in Exhibit 2.6 . |