Bivariate non-monotone dependence modeling with copulas: An application to the volume-return relationship

This paper introduces a novel methodology for constructing copula models capable of describing dependence structures of arbitrary form. The proposed method permits the creation of such copulas in parametric form, yielding models that are highly adaptable to a wide range of real-world data patterns. We apply this method ology to analyze the relationship between returns and trading volumes in financial markets, a phenomenon for which the existence of non-monotone dependencies is well documented in the existing literature. We show that our approach offers strong adaptability, providing a precise description of the dependence structure among the studied variables.