A Procedure of Perturbation Leading to a New Class of Asymmetric Copulas

We propose and analyze a new class of copulas (generated by two univariate functions) that exhibit asymmetric nonlinear dependence, resulting from an antisymmetric perturbation of the independence copula. Within this framework, we construct a parametric subclass of asymmetric copulas for which we derive the analytical expression of Kendall’s tau (τ). We present properties related to asymmetry and dependence measures, and provide several examples. To the best of our knowledge, this novel feature of our class represents a significant advancement in the context of the most studied perturbed copulas, which have been recently the focus of numerous scientific investigations.