Monte Carlo simulation

Monte Carlo simulation is a computational method for propagating uncertainty through a model. Instead of calculating one outcome from one set of assumptions, it repeatedly samples values from specified probability distributions and produces a distribution of possible outcomes. It can clarify risk, but it cannot make weak assumptions true.

When to use it

Use Monte Carlo simulation when several uncertain inputs interact and a decision depends on the range, likelihood or tail of resulting outcomes.

It is useful for product launches, investment appraisal, acquisition, project duration and cost, capacity, insurance and engineering. It helps answer:

• Which launch has the most attractive risk-adjusted outcome?
• What range of returns could an investment produce?
• Which acquisition assumptions drive downside?
• How long might a complex project take, and what budget contingency is justified?

Use simpler sensitivity analysis when only a few scenarios matter or reliable distributions cannot be estimated.

Origins

The modern method was developed at Los Alamos during and after the Second World War by researchers including Stanisław Ulam, John von Neumann, Nicholas Metropolis and Robert Richtmyer. Random sampling helped solve otherwise intractable physical calculations. The name refers to Monte Carlo’s association with games of chance, not to a claim that the method is gambling.

What it is

A simulation begins with a causal model. Uncertain inputs receive distributions that represent plausible values and their likelihoods. The computer samples a value for each input, calculates the outcome and repeats the process many times.

For a new plant, completion might plausibly occur in 12. months, 14 months, 16 months or 24 months, but those points alone do not define a distribution. Analysts must choose its shape, bounds and dependencies from evidence and expert elicitation.

The output can show expected results, percentiles, threshold probabilities and tail losses. It does not automatically show the “best case” and “worst case”: unbounded or poorly specified distributions can produce implausible extremes, while omitted risks never appear.