Monte Carlo Simulation
Simulate thousands of possible price paths using geometric Brownian motion
Simulation Parameters
Historical average return or expected return
Annual standard deviation of returns
More simulations = more accurate but slower
Simulation Results
Configure parameters and run simulation
Results will appear here
Monte Carlo Simulation Explained
What is Monte Carlo Simulation?
Monte Carlo simulation uses random sampling to model uncertainty in financial outcomes. It generates thousands of possible price paths based on expected return and volatility, providing a distribution of potential outcomes rather than a single prediction. This helps assess risk and probability of different scenarios.
Geometric Brownian Motion
The simulation uses geometric Brownian motion (GBM), the same model underlying Black-Scholes. GBM assumes that percentage returns are normally distributed and that prices follow a log-normal distribution. Formula: dS = μS dt + σS dW, where μ is drift, σ is volatility, and dW is random noise.
Key Parameters
Drift (μ): Expected annual return. Use historical average or future estimate.
Volatility (σ): Annual standard deviation. Higher = wider range of outcomes.
Time Horizon: Investment period. Longer periods increase uncertainty.
Simulations: More simulations = more accurate statistics but slower computation.
Practical Applications
Use Monte Carlo for:
- Portfolio risk assessment
- Option pricing and hedging
- Retirement planning scenarios
- Value at Risk (VaR) calculations
- Stress testing investments
Important Limitations
- Assumes returns are normally distributed (real markets have fat tails and skew)
- Assumes constant volatility (volatility clusters in real markets)
- Does not account for dividends, splits, or corporate actions
- Past volatility may not predict future volatility
- Results are probabilistic, not predictions - actual outcomes will vary