Options
Options Greeks Calculator
Black-Scholes delta, gamma, theta (per day), vega, and rho.
How the calculation works
Greeks are analytic derivatives of the Black–Scholes–Merton price. Theta is shown per calendar day (annual ÷ 365). Vega is per 1 volatility point (1%). Rho is per 1 percentage point of rate. Units are dollars of option value per contract share (multiply by multiplier × contracts for position Greek).
Formula & example
Δ, Γ, Θ, ν, ρ from Black–Scholes–Merton with continuous yield q
ATM call, S=K=100, T=1, r=5%, q=0, σ=20% → delta near ~0.64, positive gamma, negative theta.
Why use this calculator
Price alone does not show how the option moves with spot, vol, time, or rates. Greeks make those sensitivities explicit.
When to use it
Use when you need a model sensitivity snapshot for educational hedging or risk discussion under stated IV and rates.
Background
Greeks are standard risk measures derived from the Black–Scholes framework and widely used in options risk management education.
Tips for accurate results
- Per-share Greeks — multiply by 100 for a standard equity contract.
- Model Greeks ≠ exchanged-assigned or broker “position Greeks” if they use different IV surfaces.
FAQ
Why is ATM call delta not 0.50?
With positive rates (and time), forward is above spot, so ATM-spot call delta is typically above 0.5 when q is small.