Gamma (Γ)

The rate of change of delta with respect to the spot price — the curvature of the option's value.

Gamma measures how much delta changes per $1 move in the underlying: Γ = e^(−δT)·n(d₁) / (Sσ√T), where n(·) is the standard normal PDF. Gamma is always positive for long options (both calls and puts). Gamma is highest for ATM options near expiry. High gamma means the delta hedge must be rebalanced frequently ('gamma scalping'). Short options positions (gamma < 0) profit when the underlying stays still but lose from large moves.

Formula

\Gamma = \frac{e^{-\delta T} n(d_1)}{S \sigma \sqrt{T}}

Related Terms

Delta (Δ)

The sensitivity of an option's price to a $1 change in the underlying spot price.

Vega (ν)

The sensitivity of an option's price to a 1% change in implied volatility.

Theta (Θ)

The rate at which an option loses value as time passes — time decay per calendar day.

Black-Scholes-Merton Model (BSM)

The foundational option pricing formula that gives the fair value of a European call or put as a function of spot, strike, rate, volatility, and time.