Monte Carlo Simulation

Some risks are too complex for a simple formula. Monte Carlo avoids the problem by experiment. The analyst describes each uncertain input with a probability distribution, for example interest rates, project costs or loss sizes, and links them in a model. A computer then draws random values for each input, calculates the result, and repeats this thousands or millions of times. The collected results form a distribution, from which one can read the average, the worst 1% and the chance of missing a target. It is used for market risk, credit portfolios, operational risk capital, project schedules and pension funding. Results are only as good as the assumed distributions and the links between inputs, and correlations are easily misjudged. Decision makers see the spread of outcomes rather than a single best guess, and can size reserves to the odds.

A construction firm is unsure about the cost of a large project because steel prices, labour rates and delays all vary. It builds a model with a range for each and runs 10,000 trials. The output shows a 20% chance of overspending the budget, so management adds a contingency reserve.