Portfolio value at risk with Copula-ARMAX-GJR-GARCH model: Evidence from the gold and silver futures

In the article, we construct the copula-based VaR-ARMAX-GJR-GARCH model. The purpose is to examine the strategic commodities comovements and directional relationships with these variables, as well as estimating the VaR of a gold and silver portfolio. Based on our empirical results, we conclude that the crude oil for the gold and silver price in Comex and Tocom market is both a significant and positive sign whether before or during uptrend. As to US/Japan yen exchange rate, there is still no consistent result. That is to say there is no evidence that an influence of the variable to gold and silver futures exists. In addition, the time-varying SJC copula, which allows for different dependence in the tails, produced the best result regardless of being before or during uptrend. Furthermore, concerning risk management, copula-based models more accurately assess portfolio risk.