On Some Bivariate Copula Transformations

Phuong Le, Nguyen Kim Thai Ngoc

Abstract

Copulas are known as a fundamental tool to model dependence phenomena and have various applications in finance and risk management. In this paper, we propose a new class of copulas generated by means of function compositions of each two in three well-known bivariate copulas: the independence copula, the Fr\'{e}chet-Hoeffding lower bound, and the Fr\'{e}chet-Hoeffding upper bound. As consequences, we classify all