Modeling Correlation Structure for Collateralized Debt Obligations

Abstract

Pricing complex financial derivatives such as collateralized debt obligations (CDO) is considered as the main reason triggering the 2008 financial crisis. The correlation structure related to the credit risks involved in a portfolio for pricing issues have been tried to overcome via a Gaussian copula framework first introduced by David Li (2000). This approach regards the correlation among the credit risks as normally distributed (tied with a Gaussian copula framework), enabling us to derive analytical solutions. However, despite its simplicity, this approach is far from reality, which caused mispricing of the tranches of CDOs. This phenomenon is called the correlation smile. This paper takes the correlation smile issue by considering a Levy copula framework. When this is introduced to pricing equations, one can see that the correlation smile is “corrected”. Thus, a more accurate model of pricing the above-mentioned tranches is introduced.