Black-Scholes Option Pricing Calculator
Price European call and put options using the Black-Scholes-Merton model with the cumulative normal distribution function.
Results
What is it?
The Black-Scholes-Merton model is the foundational formula for pricing European-style options. It calculates the fair value of call and put options based on five inputs: stock price (S), strike price (K), time to expiry (T), risk-free rate (r), and volatility (σ). The model uses the cumulative standard normal distribution N(x) to estimate probabilities of finishing in-the-money.
How to use
Enter the current stock price, the option strike price, time to expiry in years, the risk-free interest rate (%), and the annualized volatility (%). The calculator outputs call and put prices as well as the intermediate dâ‚ and dâ‚‚ values.
Example scenario
S = $100, K = $105, T = 0.5 years, r = 5%, σ = 20%. r = 0.05, σ = 0.20. d₠= [ln(100/105) + (0.05 + 0.02)×0.5] / (0.20×√0.5) ≈ −0.0961. d₂ = d₠− 0.1414 ≈ −0.2375. Call ≈ $4.21, Put ≈ $6.63.
Pro tip
The model assumes constant volatility and no dividends. For dividend-paying stocks, use the modified Black-Scholes (reduce S by PV of dividends). Implied volatility can be backed out by inputting the market option price and solving for σ.