Geometric Brownian Motion
Geometric Brownian Motion (GBM) is a continuous-time stochastic process used to model the random evolution of quantities that cannot become negative, such as stock prices or asset values. It is defined by a stochastic differential equation that incorporates both a deterministic drift component and a random diffusion component driven by Brownian motion. GBM is widely applied in mathematical finance, particularly in the Black-Scholes model for option pricing and in risk management.
Developers should learn GBM when working in quantitative finance, algorithmic trading, or financial modeling applications, as it provides a foundational model for simulating asset price dynamics and pricing derivatives. It is essential for implementing Monte Carlo simulations, risk analysis tools, and financial forecasting systems, where capturing the log-normal distribution and volatility of asset returns is critical.