Brownian Motion in Finance

Brownian motion, or the Wiener process, is a continuous-time stochastic process used to model the random path of asset prices over time. It assumes that price changes are independent and normally distributed, serving as the mathematical backbone for the Black-Scholes option pricing model.

In this framework, the market is viewed as having no memory, meaning past price movements do not predict future ones. While real-world financial data often exhibits fat tails and volatility clustering that deviate from pure Brownian motion, it remains the standard starting point for derivative valuation.

Understanding this concept is necessary for grasping how risk is quantified and how the probability of reaching certain price levels is calculated in financial engineering.