Value at Risk for High-Dimensional Portfolios : A Dynamic Grouped-T Copula Approach

Daul et al. (2003), Demarta and McNeil (2005) and Mcneil et al. (2005) underlined the ability of the grouped t-copula to take the tail dependence present in a large set of financial assets into account, particularly when the assumption of one global parameter for the degrees of freedom (as for the standard t-copula) may be over-simplistic. We extend their methodology by allowing the copula dependence structure to be time varying and we show how to estimate its parameters. Furthermore, we examine the small samples properties of this estimator via simulations. We apply this methodology for the estimation of the VaR of a portfolio composed of thirty assets and we show that the new model outperforms both the constant grouped-t-copula and the dynamic student's T copula when long positions are of concern. As for short positions, instead, a dynamic multivariate normal model is already a proper choice