Smooth nonparametric Bernstein vine copulas

We consider the problem of accurately modelling the distribution of the market risk of a multivariate financial portfolio. We employ a multivariate GARCH model in which the dependence structure between the assets is modelled via a vine copula. We address the problem of how the parametric pair-copulas in a vine copula should be chosen by proposing to use nonparametric Bernstein copulas as bivariate pair-copulas. An extensive simulation study illustrates that our smooth nonparametric vine copula model is able to match the results of a competing parametric vine model calibrated via Akaike’s Information Criterion while at the same time significantly reducing model risk. Our empirical analysis of financial market data demonstrates that our proposed model yields Value-at-Risk forecasts that are significantly more accurate than those of a benchmark parametric model.