Chapter 6. Smoke and Mirrors: Managing Gamma through Volatile Markets

Gamma is the rate of change of the delta of an option, with respect to the underlying asset: the "delta's delta." Gamma is also expressed as the curvature of an option, or the rapidity at which the delta of an option changes as the value of the underlying asset changes. Gamma is the chief characteristic of all financial instruments that have a nonlinear payoff stream, including options. Without curvature, the sphere of financial derivatives simply would not exist. Option gamma is typically articulated as delta gained or lost per one point change in the underlying asset (also known simply as "the underlying"), with delta increasing by the amount of gamma when the underlying increases, and falling by the same amount of gamma when the underlying decreases.

Gamma indicates how steady your delta is. A large gamma indicates an unsteady delta. When gamma is high, delta can begin changing dramatically from even a small move in the underlying. Long calls and long puts always have positive gamma. Short calls and short puts always have negative gamma. Stocks, or any underlying asset, possess 0.00 gamma because their delta is always 1.00—it never changes. Positive gamma indicates that the delta of a long call will become more positive and move toward 1.00 when the underlying rises and less positive and move toward 0.00 when the underlying price falls. The delta of a long put will become more negative and move toward −1.00 ...

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