Gamma, the first derivative of Delta, indicates the change in Delta as the underlying asset price changes. Gamma is the rate of change in an option’s delta per one unit move in the underlying asset price. Gamma is an important measure of the convexity of option’s value, in relation to the underlying.
To illustrate, imagine you are driving at 70 km/h (velocity), and you are going to speed up by 10km/h to 80km/h. The velocity of the car is similar to an option’s delta value, the Gamma is the change of the velocity (or acceleration). Both Delta and Gamma are dynamic measurements.
Characteristics of Gamma：
The Gamma value is always positive regardless of whether you buy an option (no matter it is a call or a put), and the Gamma value is always negative when you sell an option.
The moneyness of an option affects the Gamma value, as the underlying price moves towards the strike price, the Gamma will rise; as the price goes further in-the-money or out-of-the-money, the Gamma will fall.
The Gamma value is also affected by the time left to expiry. As an option approaches its expiry, Gamma of the at-the-money option will be close to infinity as the expiration approaches, while the gamma of in-the-money and out-of-the-money will increase first and then decrease and reduce to zero as it approaches expiry.
The effect of volatility on Gamma is that the gamma will fall if volatility decreases and rise if volatility increases.