Pricing CDO With Levy Factor Copula Models

Collateralized Debt Obligation is a special kind of Asset-Backed Security,which is the most innovatory financial product in the end of 20 th century,and is in high favor with investors and financial institution.However,the drawbacks of credit derivatives resulted in the financial crisis in 2007,and the investors began to realize the existence of the imperfection of CDO pricing framework used in industry.The BET model and factor copula model are the most popular models in CDO pricing.However,there are some drawbacks in these models.Accordingly,we combine the existing research,and try to construct a valid pricing model for CDO and credit derivatives.This paper is consist of five parts.The first part is the introduction.We introduced the background and the significance of this research,and made a summary of past research findings.In the second part,we introduce the structure of CDO and the Large Pool Hypothesis and no arbitrage theory in CDO pricing.In the third part,we introduced the Levy Factor Copula Model,which combined the mixed VG distribution,mixed NIG distribution and factor copula model.Moreover,a concept of Forward Default Probability was introduced to build a dynamic model,and related numerical method was given,too.The fourth part is the numerical analysis and empirical analysis based on the iTraxx Europe Index Tranche.The last part is the summary of this paper.The results of this paper are as follows: we introduced the mixed VG distribution and the mixed NIG distribution,which have the property of fat tails and convolution invariance,and a factor copula model with fat-tail correlation was build based on these distributions.The pricing formula and numerical method of each CDO tranche was derived under the Large Pool Hypothesis and Levy Factor Copula Model.Aimed at the drawback of static model,we built a dynamic based on Forward Default Probability,and introduced related numerical methods.From the numerical analysis,we found the Levy distribution is the better model for default probability and default correlation modeling.At the same time,the empirical results showed that the Levy Factor Copula Models are more accurate and stable.