Modeling Asymmetric Dependence of Financial Returns with Multivariate Dynamic Copulas

Abstract

We propose a multidimensional extension for Patton’s (2006) bi-variate Dynamic Copulas. We also introduce a Dynamic Mixture Copula whose parameters and weights follow well defined dynamic processes. Both approaches improve the Copulas’ flexibilities and their adaptabilities to financial data. We utilize one G7 Stocks and one Multi-Asset Classes dataset to demonstrate the advantages of the proposed Dynamic Copulas. The object of interest are the accuracies of out-of-sample one-week portfolio Value-at-Risk (VaR) and Conditional-Value-at-Risk (CVaR) predictions and the time-instability of financial market correlations. From our empirical analyses we report three main findings. First, Dynamic Copulas which explicitly account for left tail dependence tremendously improve the portfolio VaR and CVaR forecasts for both datasets. Second, severe negative Stock market returns occur jointly with intensifying volatility levels and tightening dependencies what eliminates diversification effects when they are needed the most. Diversification among multiple asset classes significantly reduces the risk of correlation meltdowns and hence the probability of joint price drops. Third, the Euro introduction increased the correlations of the German, the Italian and the French Stock markets to about 0.9.