The copula based on multivariate t-distribution with vector of degrees of freedom

In this paper we construct a copula based on the multivariate t-distribution with vector degrees of freedom parameter, which possesses significant advantages over the copula based on the standard multivariate t-distribution. We derive the standardized version of this copula, which is simpler from the computational viewpoint. As the application of the standardized t-copula with vector of degrees of freedom we consider VAR-MGARCH models. Such models are often used for multivariate analysis of asset returns on financial markets. We also propose an algorithm of simulating random vectors with multivariate t-distribution or t-copula with vector of degrees of freedom.