GBM Asset Price Simulator

An interactive simulator for asset price paths based on Geometric Brownian Motion (GBM), built in Python. Parameters are estimated from historical data via Yahoo Finance.

What it does

The model simulates a large number of possible future price paths for any publicly traded asset. At each time step, the price evolves according to: S(t + dt) = S(t) * exp((μ - σ²/2) * dt + σ * √dt * Z)

where Z ~ N(0,1). The term σ²/2 ensures that the simulated process has expected return exactly equal to μ, accounting for the difference between arithmetic and geometric compounding.

mu and sigma are estimated from 10 years of historical log-returns and used as default values, but can be adjusted interactively.

Output

• Left panel: simulated price paths over the selected horizon
• Right panel: distribution of terminal prices across all scenarios

Parameters

Parameter	Description	Default
ticker	Yahoo Finance ticker symbol	user input
n_years	Simulation horizon (years)	10
n_scenarios	Number of simulated paths	100
mu	Annualized expected return	estimated from data
sigma	Annualized volatility	estimated from data
equity	Starting price	last closing price

Requirements

pip install pandas numpy matplotlib yfinance ipywidgets

Run in a Jupyter notebook or JupyterLab environment.