Multivariate Copula: An Application to Emerging Financial Markets

In this study, we examine the dependence structure of 20 financial markets, including 19 emerging financial markets and the US financial market, using the multivariate conditional copula of two types: the Gaussian copula and the Student’s t-copula. To adapt the multivariate conditional copulas to the high-dimensional portfolio containing 20 series, we replace the bivariate BEKK representation, used by the copula of Patton (2006) with the DCC specification of Engle (2002). Utilizing the flexibility of a copula function, we construct 12 copula types, each of which is formed by a choice of the GARCH(1,1) or the GJR(1,1,1) for the marginal model assumed by Gaussian or Student’s t or Hansen’s skewed Student’s t-distribution to be coupled with the Gaussian or the Student’s t-copula. These 12 copulas are estimated by the ‘Inference Functions for Margins’ method (IFM) which is performed via 2-step maximum likelihood estimation. The evaluation of copulas is carried out by using the AIC, the SBIC for in-sample fit and diagnostic test statistics based on the Value-at-Risk theory are used for the evaluation of out-of-sample fit. The results, indicating that the Student’s t-copula with the GARCH- t margin passes the VaR-based test and is ranked in top place in all evaluations, show that the Student’s t-copula is an appropriate method to model financial dependence. Besides, the relevant choice of a univariate GARCH model for the margin has a significant impact on the performance of the copulas. The result of our study is important for financial authorities who are concerned by financial contagions and for international portfolio managers who need a precise estimator for the Value at Risk of their portfolios.