Tail dependence of the Gaussian copula revisited

In this paper we urge that the classical measures of tail dependence may underestimate the level of tail dependence in copulas. For the Gaussian copula, however, we prove that the classical measures are maximal. The implication of the result is two-fold: On the one hand, it means that in the Gaussian case, the (weak) measures of tail dependence that have been reported and used are of utmost prudence, which must be a reassuring news for practitioners. On the other hand, it further encourages substitution of the Gaussian copula with other copulas that are more tail dependent.