Multivariate Copulas for Financial Modeling

Although the copula literature has many instances of bivariate copulas, once more than two variates are correlated, the choice of copulas often comes down to selection of the degrees-of-freedom parameter in the t -copula. In search for a wider selection of multivariate copulas we review a generalization of the t -copula and some copulas defined by Harry Joe. Generalizing the t -copula gives more flexibility in setting tail behavior. Possible applications include insurance losses by line, credit risk by issuer, and exchange rates. The Joe copulas are somewhat restricted in the range of correlations and tail dependencies that can be produced. However, both right- and left-positive tail dependence is possible, and the behavior is somewhat different from the t -copula.