The delta measures the change in the option price for a given change in the underlying.
The gamma measures the change in delta for a given change in the underlying. The long call options (both call and put) have a positive gamma and short options have a negative gamma.
The at the money call and put options have a delta of 0.5 and -0.5 respectively and the gamma is the highest at this point. As the underlying price moves away from the at the money strike the gamma decreases for both call and put options.
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