Forecasting the Risk of Speculative Assets by Means of Copula Distributions

The GARCH(1,1) model and its extensions have become a standard econometric tool for modeling volatility dynamics of financial returns and port-folio risk. In this paper, we propose an adjustment of GARCH implied conditional value-at-risk and expected shortfall forecasts that exploits the predictive content of uncorrelated, yet dependent model innovations. The adjustment is motivated by non-Gaussian characteristics of model residuals, and is implemented in a semiparametric fashion by means of conditional moments of simulated bivariate standardized copula distributions. We conduct in-sample forecasting comparisons for a set of 18 stock market indices. In total, four competing copula-GARCH models are contrasted against each other on the basis of their one-step ahead forecasting performance. With regard to forecast unbiasedness and precision, especially the Frank-GARCH models provide most conservative risk forecasts and out-perform all rival models.