Option Greeks

Brian Lee
Aug 12, 2025
Part of: Option

The major option Greeks estimate how an option’s price responds to different market factors. Derived from models such as Black-Scholes-Merton (BSM), they are typically denoted by Greek letters and help traders understand risk and reward.

Definitions

The partial differential equation (PDE) form of BSM for the option price \(V(S, t)\) is:

\[ \frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r S \frac{\partial V}{\partial S} - r V = 0 \]

Option Delta (Δ)

Expected change in the option price for a $1 move in the underlying asset.

\[ \Delta = \frac{\partial V}{\partial S} \]

Option Gamma (Γ)

Rate of change in delta as the underlying price moves.

\[ \Gamma = \frac{\partial^2 V}{\partial S^2} \]

Option Theta (Θ)

Amount of value the option loses each day from time decay.

\[ \Theta = \frac{\partial V}{\partial t} \]

Option Vega (ν)

Sensitivity of the option price to shifts in implied volatility.

\[ \nu = \frac{\partial V}{\partial \sigma} \]

Option Rho (ρ)

Measures how option prices respond to interest rate changes.

\[ \rho = \frac{\partial V}{\partial r} \]

Quiz

Test your knowledge with the Option Greeks Quiz.