Table of Contents
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.