A Unified Copula Framework for VaR forecasting

This paper examines different multivariate models to evaluate what are the main determinants when doing VaR forecasts for a portfolio of assets. To achieve this goal, we unify past multivariate models by using a general copula framework and we propose many new extensions. We differentiate the models according to the choice of the marginals distribution, the specification of the conditional moments of the marginals, the choice of the type of copula, the specification of the conditional copula parameters. Besides, we consider also the effects of the degree of assets’ riskiness, the portfolio dimensionality and the time sample used for VaR backtesting. The calculated VaR values are then compared using three different testing procedures, including Kupiec’s unconditional coverage test, Christoffersen’s conditional coverage test and a recent bootstrap test of Superior Predicting Ability proposed by Hansen (2005) and Hansen and Lunde (2005)