Estimation of VaR Using Copula and Extreme Value Theory

Abstract

This paper proposes a method for estimating the VaR of a portfolio based on copula and extreme value theory. Each return is modeled by ARMAxGARCH models with the joint distribution of innovations modeled by copula. The marginal distributions are modeled by the generalized Pareto distribution in the left tail (large loss) and empirical distribution otherwise. The copula is estimated by an estimator which gives more weight to observations with large loss. The method is applied to a two-asset portfolio and compared to other traditional methods.