Computation of value-at-risk for nonlinear portfolios

Abstract

In this paper, the authors propose saddlepoint approximation methods for fast and accurate computation of value-at-risk in large complex portfolios. The method is applicable to portfolios whose value may be estimated by means of a "delta-gamma" approximation based on a large number of underlying risk factors whose random vector of returns has a known multivariate normal distribution for the time period under consideration. This method is not subject to the statistical uncertainty and computational expense of the Monte Carlo method. Some extensions of the method to higher-order portfolio approximations and to nonnormal risk factors are also given.