Gamma

Formally, gamma is the second partial derivative of the option price with respect to
the underlying price. The units in which gamma is expressed depend on the units of
the underlying. If the underlying is expressed in small units (Nikkei average), gamma
will be a larger number. If the underlying is expressed in larger units (dollar–mark),
gamma will be a smaller number.
Gamma is typically greatest for at-the-money options and for options that are close
to expiry. Figure 1.16 displays the gamma for a typical call option.
Gamma is important because it is a guide to how readily delta will change if there
is a small change in the underlying price. This tells dealers how susceptible their
positions are to becoming unhedged if there is even a small change in the underlying
price.