Before revision: We argue that the classical indices of tail dependence quite often underestimate the tail dependence in copulas and thus may not always convey useful information. We illustrate this phenomenon using a number of bivariate copulas and suggest an alternative way for assessing taildependence .
After revision: We argue that the classical indices of tail dependence quite often underestimate the tail dependence in copulas and thus may not always comply with the new paradigm of prudent risk management. This phenomenon holds in the context of both symmetric and asymmetric copulas with and without singularities. As a remedy, we introduce a notion of paths of maximal (tail) dependence and utilize it to propose several new indices of tail dependence. The suggested new indices are conservative, conform with the basic concepts of modern quantitative risk management, and are able to distinguish between distinct risky positions in situations when the existing indices fail to do so .