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Theta (Θ)

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

Theta represents the daily erosion of an option's time value holding all else constant. For long options, theta is typically negative (the option loses value as expiry approaches). Theta is largest (most negative) for ATM options near expiry. The relationship between theta and gamma is fundamental: for a delta-neutral position, P&L ≈ ½Γ(ΔS)² − Θ·Δt. Long gamma positions (pay theta) profit from large moves; short gamma (collect theta) profit from calm markets.

Formula
Θ≈−Se−δTn(d1)σ2T−rKe−rTN(d2)\Theta \approx -\frac{S e^{-\delta T} n(d_1) \sigma}{2\sqrt{T}} - rKe^{-rT}N(d_2)

Related Terms

Delta (Δ)

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

Gamma (Γ)

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

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.