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We propose a copula-based measure of asymmetry between the lower and uppertail probabilities of bivariate distributions. The proposed measure has asimple form and possesses some desirable properties as a measure of asymmetry.The limit of the proposed measure as the index goes to the boundary of itsdomain can be expressed in a simple form under certain conditions on copulas. Asample analogue of the proposed measure for a sample from a copula is presentedand its weak convergence to a Gaussian process is shown. Another sampleanalogue of the presented measure, which is based on a sample from adistribution on $\mathbb{R}^2$, is given. Simple methods for intervalestimation and nonparametric testing based on the two sample analogues arepresented. As an example, the presented measure is applied to daily returns ofS&P500 and Nikkei225.

Copula-based measures of asymmetry between the lower and upper tail probabilities