Question

What is gamma of a stock option? How will the gamma change as the option changes from being at the money to being deeply in the money? Explain.

Answer 1

Gamma is the rate of change of the options's delta per unit change in underlying. It is the first derivative of delta with respect to price of underlying. It can also be seen as second derivative of options price with respect to change in price of underlying. When the option is at or near the money, then it is highest but when it is deep out of money or in the money, then it is small. Long position in options have a positive gamma and vice versa. Gamma decreases as it goes from at the money to deep in the money. A deep in the money option has delta close to one,(-1 for puts) hence its gamma becomes very small as there is not much room for delta to change for small movements.