Options
Black-Scholes Option Pricing Calculator
Price European call and put options with the Black-Scholes-Merton model from spot, strike, days to expiry, rate, volatility and dividend yield.
Call theoretical price
$10.45
- Call price
- $10.45
- Put price
- $5.57
Black-Scholes-Merton with continuous dividend yield. European exercise.
How this is calculated
The Black-Scholes-Merton price uses:
d1 = [ln(S/K) + (r − q + σ²/2)·T] ÷ (σ·√T)d2 = d1 − σ·√TCall = S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2)Put = K·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1)
Time T is days ÷ 365, and rates and volatility are decimals. We use a high-precision normal CDF so the price is accurate to many decimal places.
Frequently asked questions
- What does the Black-Scholes model calculate?
- It gives the theoretical fair value of a European call or put from the spot price, strike, time to expiry, risk-free rate, volatility and dividend yield.
- What are its assumptions?
- It assumes European exercise, constant volatility and rates, lognormal returns and no transaction costs — so real prices can differ, especially for American options.