Verifying the Rényi dependence axioms for a non-linear bivariate comovement index

In a paper appeared some years ago, an index for evaluating the non-linear bivariate comovement between two asset prices has been proposed. In this paper, we assess if that index satisfies the classical seven axioms formulated by Rényi that a measure of dependence should meet. In the cases in which the index does not fulfil an axiom, we propose a weakened version of that statement the index satisfies.