Monte Carlo simulation uses repeated random sampling to model probability of different outcomes in uncertain processes. Named after the Monaco casino, it was developed during the Manhattan Project for modeling nuclear physics. In finance, it generates thousands of simulated future scenarios based on probability distributions for stock returns, interest rates, and other variables. Unlike analytical formulas like Black-Scholes that give one precise answer, Monte Carlo handles complex, path-dependent problems with multiple correlated risk factors. A typical institutional risk system runs 10,000-100,000 simulated scenarios nightly to calculate risk metrics.

The mechanics are structured: specify a stochastic process for each risk factor (geometric Brownian motion for stocks), generate random shocks, apply them to calculate portfolio values at each time step. Correlations between assets use Cholesky decomposition to transform independent random variables into correlated ones. Accuracy improves with the square root of simulation count — you need 4x simulations to halve the error. Variance reduction techniques (antithetic variates, control variates) improve efficiency. Path-dependent options like Asian options, barrier options, and lookback options are natural candidates since their payoffs depend on the entire price trajectory.

In institutional risk management, Monte Carlo powers Value at Risk (VaR) and Expected Shortfall calculations that determine capital requirements. VaR at 99% confidence means: simulate 10,000+ scenarios, sort by P&L, find the loss at the 1st percentile — that's your VaR. Expected Shortfall goes further by averaging all losses beyond VaR, giving a better picture of tail risk. Banks under Basel III are required to use Expected Shortfall rather than VaR because VaR tells you nothing about how bad tail events actually get. Stress testing adds specific historical scenarios — 'what if 2008 happens again?' — to ensure survival.

Beyond risk management, Monte Carlo has applications every investor should understand. Retirement planning: instead of assuming a fixed 7% annual return, Monte Carlo generates thousands of possible paths accounting for return variability and sequence-of-returns risk. Results are expressed as probabilities — '85% chance of funding 30 years of retirement' — which is far more honest than a single projection. The institutional lesson: single-point estimates are dangerously misleading. Thinking in distributions of outcomes rather than expected values is what separates professional risk management from wishful thinking.