Gamma is the second derivative of the option’s price (premium) with respect to the underlying price/ rate. It is usually considered a measure of the curvature of the premium curve (that depicts the relationship between option price and underlying price).
Gamma = change in delta ÷ change in underlying price
Gamma measures the rate at which delta changes. It reflects the acceleration of delta, that is, the speed with which an option will go in-the-money (ITM option) or out-of-the-money (OTM option) in reaction to the change in the underlying price.
A low gamma indicates that delta would change less than proportionally when the underlying price changes. In other words, a big change in the underlying price would lead to a small change in delta. The minimum level of delta occurs when the option is in-the-money (deep in-the-money, deeper in-the-money) or out-of-the-money (deep out-of-the-money, deeper out-of-the-money), and far from the its expiration date. Low gamma works to the advantage of the option seller (the short) and against the option buyer (the long).
