Portfolio Value at Risk Bounds Using Extreme Value Theory

Abstract

The aim of this paper is to apply a semi-parametric methodology developed by Mesfioui and Quessy (2005) to derive the Value-at-Risk (VaR) bounds for portfolios of possibly dependent financial assets when the marginal return distribution is in the domain of attraction of the generalized extreme value distribution while the dependence structure between financial assets remains unknown. However, These bounds are very sensitive to location changes and depend heavily on the actual location. Modified VaR bounds are derived through an extension of the Vermaat, Does and Steerneman (2005) contribution on quantile estimation of large order to a multivariate setting which enjoy the interesting property of location invariance. Empirical studies for several market indexes are carried out to illustrate our approach.