VaR and ES Calculation with a Bayesian Dynamic tCopula-GARCH Model

The aim of the study is to calculate one-day forecasts of the Bayesian value-at-risk (VaR) and expected shortfall (ES) for two kinds of bivariate portfolios and two kinds of datasets. The Bayesian inference for VAR(1)-tCopula-GARCH(1,1), VAR(1)-tBEKK(1,1), and VAR(1)-tDCC(1,1) models and the predictive distribution of ordinary return rates of portfolio are used. The Bayesian VaR and ES fully take into account uncertainty of parameters of model. Moreover, the study also presents the one-day forecasts of VaR with using conditional autoregressive value at risk (CAViaR) with asymmetric slope and ES with employing conditional autoregressive expectiles (CARE) also with asymmetric slope. In order to compare the forecasts of VaR and ES obtained from different models, we use non-Bayesian criteria. The research shows that the calculation of VaR and ES with using tCopula-GARCH model and tBEKK model (or tDCC model for the second dataset) gives similar values of one-day forecasts, taking into account correlation coefficients between predictions from different methods. Moreover the model, which has the highest explanatory power (the highest marginal data density), not in all cases gives the best prediction the VaR and ES considering the non-Bayesian criteria.