Monte Carlo Stock Price Simulation Using Geometric Brownian Motion

Overview

This project implements a Monte Carlo simulation framework to model and forecast equity price paths using Geometric Brownian Motion (GBM). The model is applied to historical equity price data to estimate future price distributions and risk characteristics.

Methodology

• Modeled stock prices using the GBM stochastic differential equation:

  dS = μS dt + σS dW

• Estimated drift (μ) and volatility (σ) from historical log returns

• Simulated multiple price paths over a fixed time horizon

• Generated empirical distributions of terminal prices

• Computed expected return, volatility, and confidence intervals

Application

• Applied the model to NVIDIA (NVDA) historical price data
• Visualized simulated price paths and terminal value distribution
• Assessed downside risk and dispersion across scenarios

Tools & Technologies

• Python
• NumPy
• Pandas
• Matplotlib

Key Learning Outcomes

• Practical implementation of stochastic processes in finance
• Monte Carlo simulation for risk and return estimation
• Translation of continuous-time finance models into numerical simulations

Files

• Monte_Carlo_Stock_Price_Simulation.ipynb — Python notebook containing data processing, simulation logic, and visualizations