Gamma (Γ) is one of the options greeks which are collectively used to determine how closely an options or warrants contract will track its underlying market. Specifically, gamma is the rate at which the delta (Δ) of an options or warrants contract will change in relation to the price of its underlying market. Gamma is one of the second order derivatives, but because it is related to the most used first order derivative (delta), it is also one of the most useful options greeks.
Calculation
Gamma (Γ) is the second derivative of the value (V) of a single or group of options or warrants contracts (S), with respect to the price of the underlying market. Gamma is calculated as shown in the above calculation image.
Use In Trading
Gamma (Γ) is the rate that the delta of an options or warrants contract will change as the price of the underlying market increases or decreases. For example, the delta of a long put with a gamma of -0.01 will decrease by 0.01 for every increase of $1.00 (or € or £, etc.) in the price of the underlying market.
One of the most common uses of delta (not gamma), is to determine the number of options or warrants contracts that must be traded in order to approximate trading a specific number of shares (see my explanation of delta for details of this). Gamma can be used to determine the rate at which the approximation will change as the price of the underlying market changes, and can therefore be used to choose options or warrants contracts which will track their underlying market most accurately within the expected range of the underlying market.