FRM Glossary · Part I · Valuation

Black–Scholes

The closed-form option-pricing model assuming geometric Brownian motion, constant volatility, and continuous trading.

In more detail

C = S·N(d1) − K·e^(−rT)·N(d2), with d1 = [ln(S/K) + (r + σ²/2)T] / (σ√T), d2 = d1 − σ√T. Black–Scholes gives the delta, gamma, vega, theta, and rho Greeks analytically. Real markets violate the assumptions (stochastic vol, jumps, discrete trading), motivating local-vol, stochastic-vol, and jump-diffusion extensions.