A g-and-h Copula Approach to Risk Measurement in Multivariate Financial Models

We propose and backtest a multivariate Value-at-Risk model for financial returns based on Tukey's g-and-h distribution. This distributional assumption is especially useful if (conditional) asymmetries as well as heavy tails have to be considered and fast random sampling is of importance. To illustrate our methodology, we fit copula GARCH models with g-and-h distributed residuals to three European stock indices and provide results of out-of-sample Value-at-Risk backtests. We find that our g-and-h model outperforms models with less flexible residual distributions and attains similar results as a benchmark model based on Hansen's skewed-t distribution