Change Analysis of Default Correlation and Dynamic Pricing of Collateralized Debt Obligations∗

In this paper we use dynamic copulas method to price a CDO. We apply GOF test and binary segmentation procedure to detect the change of copula function. According to the result of the change point, we divide the time series into nine stages. In each stage, we use the best copula function to describe the default correlation. Our empirical results show that in different time period, the best copula fitting to data set is not static, thus the expected loss and fair spread are different for each stages. This explains why investors of CDO suffered so much when financial crisis happened. We also give a comparison among static copula model, dynamic Gaussian copula model and dynamic copula model, in the end we find dynamic copula model not only include the tail dependence in default structure, but also provide a more insensitive way to price CDO.