Explainer, in Backtesting & Validation
Monte Carlo Simulation
Monte Carlo simulation samples N paths from a probabilistic model (Brownian motion, GARCH, jump-diffusion, bootstrap-from-history), evaluates the quantity of interest on each path, and reports the empirical distribution of outcomes. Convergence rate is O(1/sqrt(N)) — quadrupling N halves the error.
1 question. Published May 10, 2026. By AI Fin Hub Research.
Definition
Monte Carlo simulation
Monte Carlo simulation samples N paths from a probabilistic model (Brownian motion, GARCH, jump-diffusion, bootstrap-from-history), evaluates the quantity of interest on each path, and reports the empirical distribution of outcomes. Convergence rate is O(1/sqrt(N)) — quadrupling N halves the error.
Why it matters
Most useful path-dependent quantities — drawdown distribution, time-to-ruin, options PnL with early-exercise — have no closed-form solution. Monte Carlo gets you a numerical answer in exchange for compute. The trade-off: the answer is only as good as the underlying model. A Gaussian Monte Carlo of crypto returns will undershoot tail risk badly.
How it works
Specify the stochastic process (parameters, distribution). Pick a seed for reproducibility. Generate N paths. Compute the path-dependent statistic on each. Report mean, median, quantiles, and the empirical distribution. Sensitivity-test by re-running with N/2 to verify convergence. Always report N, the seed, and the model assumption — without those the result isn't reproducible.
Example
Kelly-sized strategy, simulate 10,000 1-year paths
Paths
10,000
Median final equity
1.18x
5th percentile final equity
0.62x
95th percentile final equity
2.1x
Probability of >50% drawdown
8%
The mean return looks fine. The 5th percentile and the drawdown probability tell you the strategy has real ruin risk that a single backtest path would have hidden.
Key takeaways
Always seed your RNG and report the seed.
Convergence is sqrt(N) — be honest about how many paths you need for the precision you're claiming.
Garbage model in, garbage distribution out: Monte Carlo doesn't compensate for a wrong stochastic process.
Related terms
Run the numbers next
- Calculators Kelly Criterion Calculator
Size positions with full, half, quarter, or eighth Kelly and stress-test the choice with a drawdown Monte Carlo simulator. Client-side. Private by default.
- Generators Synthetic Market Data Generator
Generate synthetic price series — geometric Brownian motion, GARCH(1,1) with volatility clustering, regime-switching bull/bear, or copula-linked.
- Calculators Drawdown-Recovery Markov Simulator
Time to recover from an N% drawdown given monthly Sharpe + skew + kurtosis. Cornish-Fisher Monte Carlo, percentile distribution of recovery months.
Questions people ask next
How many paths do I need?
For median estimation, 10k is usually fine. For 99th-percentile tail estimation, 100k+. The standard error scales as 1/sqrt(N), so doubling precision needs 4x the paths. Always run a convergence check at N/2 vs N.
Sources
- Monte Carlo Methods in Financial Engineering , Glasserman (2003), Springer
Keep the topic connected
- Learn Kelly Criterion
What the Kelly criterion is, when full Kelly blows up, and why most working quants size at half- or quarter-Kelly.
- Learn Volatility
Volatility as the standard deviation of returns: realized vs implied, the annualization gotcha, and why volatility-of-volatility matters.