Remarks on composite Bernstein copula and its application to credit risk analysis

The composite Bernstein copula (CBC) (Yang et al., 2015) is a copula function generated from a composition of two copulas. This paper first shows that some well-known copulas belong to the CBC family with desirable properties. An EM algorithm for estimating the CBC is proposed, and it is applied for a real dataset to show the fitting result of the CBC in modeling dependence. The probabilistic structure for the CBC family is presented, which is useful for generating random numbers from the CBC. Finally, the probabilistic structure of the CBC is applied to credit risk analysis of collateralized debt obligations to show its advantage in empirical analysis.