A conditional approach for risk estimation

Beatriz Vaz de Melo Mendes

Abstract

ABSTRACT

Models for extreme joint tails date back to Tiago de Oliveira (1962), Pickands (1981) and Tawn (1988), and are based on limiting arguments founded on multivariate regular variation. All these models, including extreme value copulas, are designed for asymptotically dependent variables and assume that all components become large at the same rate. Heffernan and Tawn (2004) proposed a conditional multivariate extreme value model that applies to regions where not all variables are extreme and identifies the type of extremal dependence, including negative dependence. In this paper we exploit this work and provide an application in finance. The new methodology allows us to estimate new measures of financial risk, namely the conditional value-at-risk and the conditional expected shortfall given that at least one of the data components is extreme, and provides further information for portfolio selection and risk management. We illustrate using Latin American and Asian markets’ indexes, with interesting findings that are consistent but go beyond the current understanding of the interdependenciesin these emerging markets.