Credit Risk Analysis Of Collateralized Debt Obligations (CDOs)

Collateralized Debt Obligations (CDOs) are a type of structural credit derivative product. They are the transfer of credit risk, but also with greater risk. During the process of designing and issuing of the CDOs, the designing of the underlying asset pool is the key point, especially, the extent of the credit risk for the asset itself, as well as the default correlation between credit assets. They both play a decisive role in the successful issuing of the CDOs. At the same time, they will also affect the income and risk volatility of the various tranches of the structural securities issued, therefore, affecting the income of investors for all types, particularly the equity tranche holders who will first bear the risk.Therefore, it is necessary to focus on the analysis of the default risk for the underlying asset pools of CDOs, and how the default lost of the underlying asset pool affects the size of lost for each tranche of CDOs. According to the research results from predecessors about credit risk of CDOs, we can obtain two important points. One point, some scholars suggested to construct credit curve using hazard rate function, and analyze the credit derivative products with Copula. However, there is no credit risk analysis of CDOs, and also no reference to deriving credit curve by using the credit risk migration matrix. Another point, some scholars have suggested using the data of credit rating to derive credit curve, with the default probability of credit assets indicated by the time. But this method has not used the connecting Copula to analyzing the joint default risk of CDOs. Therefore, these two aspects of this research will be integrated into the analysis in this article, so that another way of analysis on credit risks of CDOs can be obtained.Firstly, one credit asset from underlying asset pool of CDOs will be taken as an example. Analyze its hazard rate function (or default probability function), and get the marginal default probability of the asset, moreover, prove that the credit curve of the credit assets was composed of a series of marginal default probabilities. Secondly, use credit risk migration matrix to derive the credit curve for each of the pool asset, and prove that this credit curve is the corresponding default time distribution of the underlying asset pool of CDOs. Thirdly, use Copula to link each credit curve of each credit asset, so as to obtain the default risk distribution based on the entire underlying asset pool of CDOs. Finally, take the phase two project of"Kai Yuan"as the object of empirical analysis, and use Markov Chain to construct credit risk migration matrix, meanwhile, use Gaussian Copula and Student-t Copula to analyze CDO comparatively. Find it that Student-t Copula can better help capture the credit default risk of CDOs, which is the same as previous research results. Therefore, the idea of this research is reasonable.