Simulations with exact means and covariances

Attilio Meucci presents a simple method to generate scenarios from multivariate elliptical distributions with given sample means and covariances, and shows an application to the risk management of a book of options

To perform risk and portfolio management, we must represent the distribution of the risk factors that affect the market. The most flexible approach is in terms of scenarios and their probabilities, which includes historical scenarios, pure Monte Carlo and importance sampling (see Glasserman, 2004).

Here, we present a simple method to generate scenarios from elliptical distributions with given sample means and covariances. This is very important in applications such as mean-variance portfolio