A New Variance Reduction Technique for Estimating Value-at-Risk

In this article we present a new variance reduction technique for estimating the Value-at-Risk (VaR) of a portfolio of various securities via Monte Carlo (MC) simulation. The technique can be applied for any type of distribution of the risk factors, no matter if light- or heavy-tailed. It consists of a particular variant of importance sampling where the change of measure is obtained by using an approximation to an optimal importance sampling density. Any approximation of the portfolio loss function (such as the popular Delta–Gamma approximation) can be used. An in-depth numerical study in the case of risk factors with light-tailed distributions exhibits a great variance reduction when estimating the probability of large portfolio losses outperforming other known methods.