Monte Carlo Simulation for Stocks, Explained from Scratch

The core idea

You want to know where a stock price might be in a year. You can't predict the future, but you can describe the range of outcomes that are consistent with how the stock has behaved before. That's what a Monte Carlo simulation does.

The technique is named after the Monte Carlo casino. The connection is randomness: just as a roulette wheel produces random outcomes, a Monte Carlo simulation generates thousands of random "what if" scenarios. Run enough of them and you start to see which outcomes are common and which are rare.

How it applies to stock prices

Stock prices change every day. Those daily changes (returns) have a distribution: most days the price moves a small amount, some days it moves a lot. If you measure a stock's historical returns, you get two numbers that matter:

• Drift – the average direction the price tends to move. A stock with positive drift trends upward over time.
• Volatility – how much the price bounces around that trend. High volatility means wider swings day to day.

With drift and volatility measured from real data, you can simulate a plausible future. Each simulated day, you generate a random return drawn from the stock's historical behaviour and apply it to the current price. Chain 252 of those together (one trading year) and you get one possible price path.

One path tells you nothing. But run 5,000 paths and patterns emerge. You can answer questions like: "What's the probability this stock finishes above its current price?" or "What's the worst 10% of outcomes?"

A simple example

Say a stock trades at £100 with 20% annualised volatility and 8% drift. You simulate 5,000 one-year paths. The results might look like this:

• Median outcome: £108 (the middle path, close to the drift)
• P90 (optimistic): £138
• P10 (pessimistic): £82
• Probability of gain: roughly 62%

None of those numbers are predictions. They're the statistical consequence of past behaviour continuing into the future. That distinction matters.

Why "5,000 paths" and not just one forecast?

A single forecast gives you a point estimate with no sense of how wrong it might be. Monte Carlo gives you the full distribution. You can see the fat tails, the skew, the probability of different outcomes. For risk management, that's far more useful than a single number.

This is why hedge funds, investment banks, and pension funds use Monte Carlo methods. They need to understand the range of possible losses, not just the expected return.

Where it breaks down

Monte Carlo simulation for stocks typically relies on a model called geometric Brownian motion (GBM). GBM assumes:

1. Returns are log-normally distributed
2. Volatility stays constant over time
3. Each day's return is independent of the last

Real markets violate all three. Crashes cluster together (volatility is not constant). Extreme moves happen more often than a normal distribution predicts (fat tails). Momentum and mean-reversion exist (returns are not fully independent).

This doesn't make Monte Carlo useless. It means you should treat the output as a rough map, not GPS coordinates. The shape of the distribution is informative even if the exact percentiles aren't precise.

For a deeper look at the GBM model and the maths behind it, see Geometric Brownian Motion: The Maths Behind Stock Price Simulation.

What you can (and can't) use it for

Try it yourself

The Monte Carlo Stock Simulator runs 5,000 simulations on any publicly traded stock using real market data. Search for a ticker, pick a time horizon, and see the full probability distribution of future prices, with confidence bands and a histogram of outcomes.