Stock Price Simulator — Geometric Brownian Motion

A Monte Carlo stock price simulator built in Python using Geometric Brownian Motion (GBM). Simulates thousands of potential price paths for a given stock and outputs key statistics and a visualisation.

How It Works

The simulator models stock price evolution using the GBM stochastic differential equation:

$$dS_t = \mu S_t \ dt + \sigma S_t \ dW_t$$

Which in discrete form becomes:

$$S_{t+dt} = S_t \cdot \exp\left(\left(\mu - \frac{\sigma^2}{2}\right)dt + \sigma \sqrt{dt} \cdot Z\right)$$

where $Z \sim \mathcal{N}(0, 1)$ is a standard normal random variable.

Requirements

• Python 3.x
• NumPy
• Matplotlib

Install dependencies with:

pip install numpy matplotlib