Black-Scholes Call Option Price Calculator

Formula: $$C = S_0 N(d_1) - X e^{-rT} N(d_2)$$
with $$d_1 = \frac{\ln(S_0/X) + (r + \frac{1}{2}\sigma^2)T}{\sigma \sqrt{T}}, \quad d_2 = d_1 - \sigma \sqrt{T}$$

Spot Price $S_0$: Strike Price $X$: Risk-Free Rate $r$ (decimal): Time to Maturity $T$ (years): Volatility $\sigma$ (decimal):

Interpretation

The Black-Scholes formula provides the fair price of a European call option under the assumptions of constant volatility and risk-free rate.
$d_1$ and $d_2$ are intermediate terms used to compute the probabilities of finishing in-the-money.
This formula is foundational for options pricing, Greeks calculation, and risk management.

Key Assumptions

Underlying asset follows a geometric Brownian motion.
Markets are frictionless (no transaction costs, taxes).
No dividends are paid during the option's life (for basic model).
Constant and known risk-free interest rate and volatility.
European exercise style (can only exercise at maturity).