Monte Carlo simulation

A Monte Carlo simulation estimates the distribution of an uncertain quantity by drawing a very large number of random scenarios and reading the answer off the resulting sample; the name is a nod to the Monte Carlo casino and the luck of the tables. Metropolis and Ulam, "The Monte Carlo Method," Journal of the American Statistical Association, 1949: the method came out of Los Alamos, where Ulam and von Neumann had developed it for neutron transport. The principle has not moved since. When a quantity depends on too many sources of uncertainty, interacting non-linearly, for an analytical answer to hold, you draw thousands or millions of scenarios, each one a possible future, and read the mean, the quantiles, VaR or TVaR off the resulting distribution. Estimation error falls as 1/√N. Cutting the error by ten takes a hundred times more draws, and the tail, where the capital number sits, is exactly where draws run thinnest. Practitioners say Monte Carlo method, Monte Carlo analysis or Monte Carlo model more or less interchangeably; strictly, the model is the set of distributions and dependencies, and the simulation is the engine that runs them. It is often confused with the bootstrap, which resamples observed data instead of drawing from chosen distributions, and with a deterministic stress scenario, which gives a single point. The method runs inside Solvency II internal models, cat models and a good many treaty pricing tools. A cat model draws years of events from its stochastic catalog and turns them into exceedance curves. Its strength is that it will swallow almost any probabilistic problem. Its limit fits on one line: the output is only as good as the distributions and dependencies fed in, and a million draws will not rescue a badly chosen copula. In cyber, where dependence between insureds is the big unknown, the results have to be read with particular caution.