Gamma is the second derivative of the option’s price 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 high gamma indicates that delta would change more than proportionally when the underlying price changes. In other words, a small change in the underlying price would lead to a big change in delta. The maximum level of delta is attained when the option is at-the-money (ATM option), and close to the its expiration date. High gamma works to the advantage of the option buyer (the long) and against the option seller (the short).
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