Monte Carlo Simulation
Stock Price Path Simulation using Geometric Brownian Motion
Source: DeepViews Simulation
Monte Carlo simulation is a computational technique that uses repeated random sampling to estimate the probability distribution of an uncertain outcome. In finance, it helps quantify the range of possible values rather than relying on a single point estimate.
By running thousands of simulations with randomly sampled inputs, we can build a probability distribution of outcomes — seeing not just the "expected" value but the full range of possibilities and their likelihoods.
This approach is especially valuable when inputs are uncertain: rather than asking "what IS the fair value?", Monte Carlo asks "what is the probability the stock is undervalued?"
dS = μS dt + σS dW
S(t) = S₀ exp((μ - σ²/2)t + σW(t))
- Set initial price, drift, and volatility from historical data
- Generate random daily returns using GBM formula
- Simulate thousands of price paths over the time horizon
- Compute percentile bands from all simulated paths
- Analyze terminal price distribution and statistics
Key Takeaway
A single fair value number creates false precision. Monte Carlo simulation embraces uncertainty by showing the full range of possible outcomes and their probabilities — turning "the stock is worth $150" into "there is a 70% probability the stock is undervalued."
Disclaimer: This is not financial advice. Data sourced from SEC EDGAR and Polygon.io. Past performance does not guarantee future results. Always conduct your own research before making investment decisions.