Motivation Given an asset’s historical prices over some time horizon (e.g., the price of APPL on each trading day of 2019), it is often of practical importance to fit a distribution to those prices. One choice of parametric model for stock prices is geometric Brownian motion (GBM). This note derives maximum likelihood estimators for the parameters of a GBM. A word of caution: a GBM is generally unsuitable for long periods. Other choices of models include a GBM with nonconstant drift and volatili...