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Gamma

In short

Rate of change of delta — how quickly delta shifts as the stock moves

Gamma measures how fast delta changes. High gamma means your option becomes more or less sensitive quickly as the stock moves. Near expiration, gamma is highest — small stock moves cause big swings in option value.

Gamma is the second derivative of option price with respect to the underlying. It's highest for at-the-money options near expiration. Long options (calls/puts) have positive gamma. High gamma creates convexity — accelerating profits when the stock moves your way.

Formula

Gamma = ∂Delta ÷ ∂Underlying Price

Related concepts

  • Delta — If a call has delta of 0.5, it gains $0.50 for every $1 the stock rises. Delta 1.0 means the option moves dollar-for-dollar with the stock. At-the-money options typically have delta near 0.5.
  • Theta — Options are like ice cubes that melt over time. Theta measures how fast value evaporates daily. An option with theta of -$0.05 loses $5 per day per contract, all else equal. Time is your enemy as an option buyer.
  • Implied Volatility — Implied volatility is the market's guess about how much a stock will move. High IV means expensive options (the market expects big moves). Low IV means cheap options. Buy options when IV is low, sell when IV is high.
  • Vega — Vega measures how much an option's price changes when market expectations of volatility change. If you expect a big announcement (earnings, FDA), buy before the event — vega will boost your option's value as uncertainty rises.