February 13th, 2003, 2:46 pm
The whole discussion on this topic so far has been concerned with normal distributions.More generally, you might want to simulate correlated numbers from an arbitrary collection of marginal distributions.This is the basic problem that insurance companies face all the time: estimating their total p+l distribution, when the individual parts of their business (different classes of insurance, investments, and so on) are correlated, and have weird and wonderful marginal distributions. The only 'derivatives' application I know is for modelling portfolios of weather derivatives, some of which may have very non-normal distributions (e.g. the number of days it snows in winter).Even given the correlations, there is no unique answer, unlike for the normal case.The standard method used in practice is due to Iman and Connover.My understanding of it is that it works as follows:1)calculate rank correlations2)convert them to linear correlations using a cunning formula3)simulate (using Choleski or SVD) from a multivariate normal with these correlations4)convert the normally distributed simulations to the right marginal distributions using the CDF of the normal distribution and the inverse CDF of the marginal distribution.To go further than this, you could start looking at copulas.Sloth