Definition of Gamma

Gamma is the rate of change of delta of an option, in response to changes in the prices of an underlying asset. It gives us a significant evaluation of convexity of a future contract’s value, with respect to the underlying assets.

Points to remember:

• A positive gamma depicts an affirmative convexity of trading position.
• In order to preserve a hedge over a wide price range, a delta hedge plan involves reducing gamma. However, a major outcome of reducing it is that, alpha too, is reduced.

Example:
Let us assume that a call option on an underlying stock has a delta of 0.4. If the value of that stock goes up by $1, the option’s value increases by $0.40, inevitably changing its delta to 0.53. The 0.13 difference in deltas is measured as an estimated gamma value.