Geometric Brownian Motion (GBM) Simulator

GBM models asset prices as: $$dS_t = \mu S_t dt + \sigma S_t dW_t$$ where μ = drift, σ = volatility, W = Wiener process.

Initial Price S₀: Drift μ (decimal): Volatility σ (decimal): Time Horizon T (years): Number of Steps: Number of Simulations: Number of Paths to Plot:

Interpretation

GBM assumes continuous compounding with drift μ and volatility σ.
Simulations provide probabilistic distribution of asset prices and returns.
Useful for Monte Carlo pricing, VaR, and scenario analysis.

Key Assumptions

Continuous paths (no jumps).
Constant drift μ and volatility σ.
Random shocks are normally distributed and independent.
No arbitrage, frictionless market.