Gamma

Gamma is the measure of change of a portfolio’s delta with respect to the change in the price of the underlying asset; where delta is the change in the price of an option due to change in the price of the underlying asset. In other words, gamma is the second partial derivative of the portfolio with respect to the underlying asset price.

    Gamma = Change in an option delta/ Unit change in price of underlying asset

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where ¶ is the value of the portfolio and S is the price of the underlying asset.

Gamma works as an acceleration of the option, i.e. it signifies the speed with which an option will go either in-the-money or out-of-the-money due to change in the price of the underlying asset. If gamma is a small number then delta changes slowly and it is easy to keep the portfolio delta neutral. However, if gamma is high, positive or negative, delta will be very price (of the underlying asset) sensitive.