Finance

Black-Scholes Option Pricing Calculator

Price European call and put options and compute all Greeks using the Black-Scholes-Merton model.

Stock Price (S) ($)

Strike Price (K) ($)

Time to Expiry (years)

Volatility (σ) (%)

Risk-Free Rate (%)

Dividend Yield (%)

Black-Scholes Formula:
C = S·e^(-qT)·N(d1) − K·e^(-rT)·N(d2)
P = K·e^(-rT)·N(−d2) − S·e^(-qT)·N(−d1)
d1 = [ln(S/K) + (r−q+σ²/2)T] / (σ√T)
d2 = d1 − σ√T

The Black-Scholes Model

The Black-Scholes-Merton model (1973) is the foundational framework for pricing European-style options. It earned Myron Scholes and Robert Merton the Nobel Prize in Economics in 1997.

The Greeks

Delta (Δ): Price sensitivity to $1 move in the underlying
Gamma (Γ): Rate of change of delta — measures curvature
Theta (Θ): Time decay — value lost per day
Vega (ν): Sensitivity to 1% change in volatility
Rho (ρ): Sensitivity to 1% change in interest rate

Model Assumptions

European exercise only, lognormal returns, constant volatility, no transaction costs, efficient markets, and continuous trading.