Geometric Brownian Motion
Geometric Brownian Motion (GBM) is a mathematical model used to describe the random movement of prices in financial markets. It assumes that the logarithm of the price follows a normal distribution, which means prices can increase or decrease over time in a continuous manner. This model is particularly useful for modeling stock prices and other assets.
GBM incorporates two key components: a drift term, representing the average rate of return, and a volatility term, indicating the degree of price fluctuations. This combination allows for the simulation of realistic price paths, making it a foundational concept in financial mathematics and option pricing theory.