Black-Scholes Option Pricing Model

A continuous‑time, arbitrage‑based model that prices European‑style options by modeling the underlying asset price S(t) as a geometric Brownian motion with constant volatility σ and constant risk‑free rate r (and optional continuous dividend yield q), deriving a closed‑form formula for the option value under the risk‑neutral measure (e.g., for a European call: C = S0·N(d1) − K·e^(−rT)·N(d2)).