Geometric Brownian Motion (GBM) is a powerful mathematical model used to understand the unpredictable behavior of various phenomena, particularly in finance. In this article, we’ll dive into the simulation of Geometric Brownian Motion and take a closer look at two commonly used numerical schemes: Euler-Maruyama and Milstein. These schemes are essential tools in approximating GBM paths and find widespread application in financial modeling and analysis. This article is accompanied by a Jupyter Notebook which provides a python implementation for the simulation of a stock price as a GBM process.

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