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TL;DR

A computational method that uses random sampling to estimate mathematical quantities. Generate many random paths or scenarios, compute the quantity of interest for each, and average the results.

By Valenke Exam Prep Team·Last updated 2026-06-03

Monte Carlo Simulation

A computational method that uses random sampling to estimate mathematical quantities. Generate many random paths or scenarios, compute the quantity of interest for each, and average the results.

Why it matters for interviews

The primary numerical method for pricing complex derivatives, estimating portfolio risk (VaR), and evaluating strategies. Understanding variance reduction techniques and convergence rates is essential for quant roles.

Definition and Mathematical Foundation

A computational method that uses random sampling to estimate mathematical quantities. Generate many random paths or scenarios, compute the quantity of interest for each, and average the results.

Application in Quantitative Finance

The primary numerical method for pricing complex derivatives, estimating portfolio risk (VaR), and evaluating strategies. Understanding variance reduction techniques and convergence rates is essential for quant roles.

Related Terms

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Frequently Asked Questions

What is the convergence rate of Monte Carlo?▼
The standard error decreases as \( O(1/\sqrt{n}) \) regardless of dimension. This dimension-independence makes Monte Carlo superior to grid methods in high dimensions (curse of dimensionality).
What are variance reduction techniques?▼
Antithetic variates (use \( W \) and \( -W \) pairs), control variates (subtract a known quantity), importance sampling (sample from a better distribution), and stratified sampling. These can reduce variance by orders of magnitude.
How is Monte Carlo used for options pricing?▼
Simulate stock price paths under the risk-neutral measure, compute the payoff for each path, discount to present, and average. For path-dependent options (Asian, barrier), Monte Carlo is often the only feasible approach.