Estimating value-at-risk using a multivariate copula-based volatility model: Evidence from European banks

Abstract

This paper proposes a multivariate copula-based volatility model for estimating Value-at-Risk (VaR) in the banking sector of selected European countries by combining dynamic conditional correlation (DCC) multivariate GARCH (M-GARCH) volatility model and copula functions. Non-normality in multivariate models is associated with the joint probability of the univariate models' marginal probabilities –the joint probability of large market movements, referred to as tail dependence. In this paper, we use copula functions to model the tail dependence of large market movements and test the validity of our results by performing back-testing techniques. The results show that the copula-based approach provides better estimates than the common methods currently used and captures VaR reasonably well based on the differences in the numbers of exceptions produced during different observation periods at the same confidence level.