A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift.[1] It is an important example of stochastic processes satisfying a stochastic differential equation (SDE); in particular, it is used in mathematical finance to model stock prices in the Black–Scholes model.
- ^ Ross, Sheldon M. (2014). "Variations on Brownian Motion". Introduction to Probability Models (11th ed.). Amsterdam: Elsevier. pp. 612–14. ISBN 978-0-12-407948-9.