Gamma
Gamma measures the rate of change of an option's delta for every $1 move in the underlying stock price — essentially the acceleration of the option's price sensitivity.
If delta tells you how much an option's price moves with the stock, gamma tells you how quickly delta itself is changing. A high-gamma option becomes dramatically more or less sensitive to stock price changes as the market moves, while a low-gamma option maintains relatively stable delta. Gamma is always positive for both calls and puts when holding long positions, because a long option benefits from increased delta as the stock moves in a favorable direction.
Gamma is highest for at-the-money options close to expiration and lowest for deep in-the-money or deep out-of-the-money options with significant time remaining. This creates the phenomenon known as 'gamma risk' or 'negative gamma' for short options sellers: a market maker or premium seller with short gamma faces accelerating losses if the stock moves sharply, because each increment of adverse movement increases the delta and thus the pace of loss.
Consider a call option with a delta of 0.50 and a gamma of 0.05. If the stock rises $1, the delta increases to 0.55. A further $1 rise pushes delta to 0.60. This compounding effect benefits long option holders — their options become more responsive to favorable moves. For sellers, it means losses compound in a rapidly trending market.
'Gamma squeeze' has entered mainstream financial vocabulary following events like the GameStop frenzy of January 2021. When a heavily shorted stock experiences a rush of call buying, options market makers who sold those calls must buy increasing amounts of underlying shares to delta-hedge as gamma pushes delta higher. This forced buying accelerates the stock's rise, triggering more gamma, more hedging, and more price appreciation in a feedback loop.
Long gamma strategies (buying straddles, buying ATM options) profit from large stock moves in either direction, at the cost of theta decay. Short gamma strategies (selling premium) profit from quiet markets but suffer disproportionate losses during volatility spikes. Managing the gamma/theta tradeoff is central to professional options portfolio management.