Python for Finance Cookbook

Simulating stock price dynamics using Geometric Brownian Motion

Thanks to the unpredictability of financial markets, simulating stock prices plays an important role in the valuation of many derivatives, such as options. Due to the aforementioned randomness in price movement, these simulations rely on stochastic differential equations (SDE).

A stochastic process is said to follow the Geometric Brownian Motion (GBM) when it satisfies the following SDE:

Here, we have the following:

• S: Stock price
• μ: The drift coefficient, that is, the average return over a given period or the instantaneous expected return
• σ: The diffusion coefficient, that is, ...