Gamma

Gamma measures how much delta changes when the underlying asset moves by one point. It describes the curvature of the option price relative to the stock price and is highest for at-the-money options near expiration.

What is gamma?

Gamma is the second partial derivative of the option price with respect to the underlying price, or the rate of change of delta. High gamma means delta shifts quickly as the stock moves. Long options have positive gamma; short options have negative gamma. At-the-money options near expiration exhibit the highest gamma, which is why delta can swing sharply in the final days before expiry.

How to measure gamma

Gamma is calculated from the same models used for delta and is displayed as the expected change in delta for a $1 move in the underlying. For example, gamma of 0.05 means delta increases by 0.05 when the stock rises $1.00. Portfolio gamma is the net sum across all legs. Market makers and hedgers watch gamma closely because it determines how often they must rebalance delta hedges as the stock moves.

How gamma changes

Gamma peaks for at-the-money options and falls for deep in-the-money or far out-of-the-money strikes. It increases as expiration approaches for at-the-money options, then drops sharply after expiry. Lower implied volatility tends to increase gamma near the strike. Calendar spreads and positions with opposing gammas can reduce net gamma exposure. Short gamma positions become harder to manage when the underlying makes large moves because delta moves against the trader quickly.

How option prices change when gamma changes

Rising gamma makes option payoffs more convex relative to the stock—long options gain delta faster on favorable moves and lose delta slower on small adverse moves near the strike. Falling gamma makes delta more stable and price changes more linear. For a long call with high gamma, a rally not only raises the premium through delta but also increases delta itself, amplifying further gains. Short gamma sellers face accelerating losses on large moves because delta moves against them. Traders use gamma to assess pin risk, hedge frequency, and how directional exposure will evolve after a move.