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Extreme value properties of multivariate t copulas

<13>Bivariate extreme value (EV) copulas can be derived using the standard techniques of EV theory. We introduce the tail dependence functions to allow the derivation in higher dimensions. They provide a powerful method for deriving multivariate EV limit distributions and tail probabilities that enable the characterization of measures of extremal dependence. We evaluate these functions for the multivariate t copula and derive the t-EV copula and the limits of the latter. We establish the sharpness of the inequality among bivariate tail dependence parameters using these limits and show t copulas cover a wide range of refection symmetric tail dependence.