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Monte Carlo Stock Price Simulation

A Monte Carlo stock simulation generates thousands of possible future total-return-equivalent price paths from a statistical process. Historical returns use split- and dividend-adjusted closes whenever available. It helps visualize uncertainty and downside ranges, but it is a probability model rather than an intrinsic value calculation or guaranteed forecast.

Monte Carlo simulation formula

S(t+1) = S(t) × exp((μ − 0.5σ²)Δt + σ√Δt × Z)

This geometric Brownian motion formula updates price S using expected drift μ, volatility σ, time step Δt and a random standard-normal value Z. Repeating the process across many paths creates a distribution of potential outcomes.

Key inputs

Starting price
The latest price in the homogeneous historical series from which every simulated path begins.
Drift (μ)
The assumed expected return, often estimated from history or replaced with a forward-looking scenario.
Volatility (σ)
The annualized standard deviation of returns and the primary driver of simulated dispersion.
Time horizon and steps
The forecast length and number of trading intervals, such as 252 daily steps for one year.
Simulation count
The number of independently generated paths; thousands of runs usually stabilize percentiles.

Monte Carlo stock simulation example

  1. 1Start with a $100 stock price, 7% annual drift and 25% annual volatility.
  2. 2Split a one-year horizon into 252 trading-day steps.
  3. 3Generate a new random standard-normal value for every step and price path.
  4. 4Repeat the geometric Brownian motion update across 10,000 independent paths.
  5. 5Summarize ending prices with percentiles instead of selecting one path.

An illustrative run might show a 10th percentile near $72, a median near $104 and a 90th percentile near $151. Exact results vary with every run and do not represent price targets.

When Monte Carlo simulation is useful

  • Visualizing a range of possible outcomes instead of relying on one forecast.
  • Understanding how volatility affects future price uncertainty.
  • Supporting scenario analysis and risk-aware investment decisions.

Limitations to consider

  • Results depend on assumptions derived from historical data.
  • If adjusted closes are entirely unavailable, the result is labeled as a raw-close fallback whose returns can be affected by splits and dividends.
  • Real markets can experience regime changes, extreme events and non-normal returns.
  • A simulation describes possible outcomes but does not determine fair value on its own.

How to calculate Monte Carlo simulation

  1. 1Collect a complete adjusted-close history over a representative observation period; never mix adjusted and raw closes.
  2. 2Calculate periodic logarithmic returns.
  3. 3Estimate or choose forward-looking drift and volatility assumptions.
  4. 4Set the horizon, time step and number of simulations.
  5. 5Generate random shocks and build each possible price path.
  6. 6Summarize median, mean, percentiles and probability thresholds.
  7. 7Repeat with bearish and bullish assumptions to test model sensitivity.

How to interpret the result

Read the output as a distribution, not a prediction. Percentiles describe modeled downside and upside ranges, while the median is the middle simulated outcome. A wide distribution signals greater uncertainty. Compare several volatility and drift scenarios and remember that tail events may be understated.

Compare related stock analysis models

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Relative Valuation

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Altman Z-Score

Add an accounting-based distress screen that a price process alone cannot capture.

Frequently asked questions

How does the simulation handle stock splits and dividends?

Historical returns use adjusted closes, which remove artificial split and ex-dividend jumps. If adjusted closes are missing for the entire series, the API and result identify the raw-close fallback. A partially adjusted series is rejected instead of being mixed.

What formula is used for Monte Carlo stock simulation?

A common approach uses geometric Brownian motion: the next price depends on current price, drift, volatility, the time step and a random normal shock.

Does Monte Carlo simulation predict a stock price?

It does not predict one certain price. It generates a probability distribution of possible outcomes based on the assumptions and process used.

How many Monte Carlo simulations are enough?

Thousands of paths are commonly used. More runs generally stabilize percentiles, although realistic assumptions matter more than an extremely high count.

What is drift in a stock simulation?

Drift is the assumed expected return component of the simulated process. Historical average return is one option, but forward-looking scenarios may be more appropriate.

Is Monte Carlo simulation a valuation model?

It is primarily a risk and scenario model. It can complement valuation work, but it does not directly estimate intrinsic business value like a DCF or DDM.

Learn the method in context

Go beyond the formula with worked explanations, assumptions and common mistakes in the Stock Insights Academy.

Read the related Academy guide

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