A first-order Greek is a first-order derivative of the option value with respect to some variable such as underlying’s price, volatility, interest rate, passage of time, etc. This means we assume that only one variable used to determine the value of an option is changed, and the remaining inputs to the option model are held constant.
First-order greeks include: delta, vega, rho, theta, and lambda. The following table summarizes the main first-order greeks:
| Variable/parameter | Symbol | Measures option’s sensitivity with respect to: |
|---|---|---|
| Delta | Δ | Change in underlying price |
| Vega | ν | Change in volatility |
| Rho | ρ | Change in interest rate |
| Theta | θ | Change in time to expiration |
| Lambda/omega | λ / Ω | Percentage change in underlying price |
For example, rho measures the option’s sensitivity to the risk-free interest rate, and hence it is the derivative of the option value with respect to the risk-free interest rate for a corresponding maturity. Likewise, lambda (or omega) represents the percentage change in the option value relative to the percentage change in the underlying price.
