Black-Scholes Calculator
The Black-Scholes model prices a European option from five inputs: stock price, strike, time to expiry, volatility and the risk-free rate. Enter them below to get the call and put value with all five greeks. Theta is per calendar day, vega per one volatility point and rho per one point of interest rate.
| Call | Put | |
|---|---|---|
| Price | 10.4506 | 5.5735 |
| Delta | 0.6368 | -0.3632 |
| Gamma | 0.01876 | 0.01876 |
| Theta / day | -0.0176 | -0.0045 |
| Vega / 1 vol pt | 0.3752 | 0.3752 |
| Rho / 1 rate pt | 0.5323 | -0.4189 |
For education only, not financial advice. Read the disclaimer.
HOW IT WORKS
d1 = (ln(S/K) + (r + sigma^2/2) T) / (sigma sqrt(T)) and d2 = d1 - sigma sqrt(T). Then Call = S N(d1) - K e^(-rT) N(d2) and Put = K e^(-rT) N(-d2) - S N(-d1), where N is the standard normal CDF and T is days divided by 365.
Delta is N(d1) for a call and N(d1) - 1 for a put. Gamma is N'(d1) / (S sigma sqrt(T)), the same for both. Theta is the annual theta divided by 365 (per calendar day). Vega is the price change for a 1 point move in volatility, and rho for a 1 point move in the rate.
The model assumes European exercise, constant volatility and rates, and no dividends. American options on dividend-paying stocks can be worth more than these values.