Inputs
Results
Enter inputs and press Calculate Greeks to see values for call and put.
Notes & Formulas
Model: Black–Scholes–Merton with continuous dividend yield q. Let
d1 = [ln(S/K) + (r - q + 0.5 σ²)T] / (σ√T) and d2 = d1 - σ√T.
- Delta: Call
e^{-qT}N(d1), Pute^{-qT}(N(d1)-1) - Gamma:
e^{-qT} n(d1) / (S σ √T) - Vega:
S e^{-qT} n(d1) √T(shown per 1% volatility) - Theta: Uses standard annual formulas; shown per day and per year
- Rho: Call
K T e^{-rT} N(d2), Put-K T e^{-rT} N(-d2)(shown per 1% rate)
All outputs are in price units of the underlying unless otherwise stated.
FAQs
Vega is the change in option price for a small change in implied volatility. Reporting per 1% means the value corresponds to a one‑percentage‑point change in volatility.
Typically yes, because time decay reduces option value. Exceptions can occur for deep in‑the‑money or high dividend situations.
Continuous dividend yield reduces the effective growth rate of the underlying. It lowers call Delta and price while raising put value compared to a zero‑dividend case.
This tool assumes 365 calendar days. Many desks use 365 or 252 depending on convention. Be consistent with your implied volatility source.
Gamma indicates how quickly Delta changes with price. Higher Gamma means more sensitivity to small moves, which increases hedging demands and risk.