Measuring the risk of a nonlinear portfolio with fat tailed risk factors through probability conserving transformation

Abstract

This paper presents a new heuristic for fast approximation of VaR (Value-at-Risk) and CVaR (conditional Value-at-Risk) for financial portfolios, where the net worth of a portfolio is a non-linear function of possibly non-Gaussian risk factors. The proposed method is based on mapping non-normal marginal distributions into normal distributions via a probability conserving transformation and then using a quadratic, i.e. Delta–Gamma, approximation for the portfolio value. The method is very general and can deal with a wide range of marginal distributions of risk factors, including non-parametric distributions. Its computational load is comparable with the Delta–Gamma–Normal method based on Fourier inversion. However, unlike the Delta–Gamma–Normal method, the proposed heuristic preserves the tail behaviour of the individual risk factors, which may be seen as a significant advantage. We demonstrate the utility of the new method with comprehensive numerical experiments on simulated as well as real financial data.