Comparative Analysis Of CDO Pricing Models

Although gaussian copula model has been a standard approach in pricing of the CDO products, structural model and reduced-form model still have their unique advantages in the CDO pricing theory. In the view of how to join the default correlation in credit portfolio, the paper gives the comparative study to the modeling mechanism of the three models in theoretical and empirical aspects. The following are the main conclusions.With respect to the reduced-form model of CDO pricing, the main content includes three aspects:firstly, it is about the theory of the reduced-form model; nextly, it is about the risky analysis of default correlation in asset portfolio, which considering from the perspective of the default intensity; finally, based on the risky analysis of credit portfolio, the paper studies the reduced-form model, and focuses on the calculation of diversity scores in idealized comparison portfolio.With respect to the application of reduced-form model, the paper gives the theoretical and empirical analysis for the application of the model in four aspects, which is based on risky model of the credit portfolio and the reference of the term structure of interest rate model:firstly, it gives some issues about the stability of the estimated parameters in theory, the conclusion shows that the traditional numerical method can not guarantee the estimators are the global maximum; secondly, it gives the comparison to the reduced-form model and the term structure of interest rates model in theory, we find that they are the same modeling method in two applying ways; thirdly, the paper gives an empirical study based on the term structure of interest rate model, which provides a reference for CDO pricing using reduced-form model in future, the conclusion shows that the stability of estimators are highly dependent on the choice of initial value using numerical methods and the result is still discussing whether it is the global maximum value of the likelihood function; lastly, the article gives the identiability of Gaussian model using Minimum-Chi-Square approach and empirical study of Gaussian term structure model, the theoretical study shows that MCS estimator and MLE are asymptotically equivalent, and we can be sure that the MCSE is global maximum, and the component of numerical computation in MCS approach is far simpler than the ML approach.With respect to copula approach of CDO pricing, beginning with the basic theory of copula function, the article gives the factor-based copula method of CDO pricing, the following are the main content:firstly, we study the two kinds of typical copula function, standard copula and Archimedes copula, starting from the basic copula theory, and give the process of random simulation; nextly, we study sampling theory of n dimensional copula function, which provides the theoretical basis for CDO simulation; lastly, it is about factor-based copula theory, the main content is about Gaussian copula model and t-copula model.With repect to structural model of CDO pricing, the base of which is first passage model, we give the risk model of credit portfolio and CDO structural pricing approach, the main content is in following:firstly, about the structural model of credit asset, we show that credit spreads is narrowing with increasing of the modified distance to default; next, the structural model of CDO pricing in credit portfolio mainly includes two parts, simulation of default barrier and structural CDO pricing. The choice of default barrier should be consistent with the distribution of first passage model and the density function of default; lastly, we give the comparison to the structural model and copula model of CDO pricing, the conclusion show that with respect to default correlation, Gaussian copula model is a reasonable approximation to that given by structural model, the two approaches are present little differences in CDO pricing.