The Pricing Of Collateralized Debt Obligations

This paper is mainly about Collateral Debt Obligations pricing methods to explore and studies factors affecting CDO prices, focusing on the analysis of default density of the underlying assets and default correlation between those assets.We firstly use the non-arbitrage methods on CDO pricing. Then under the condition of normal single factor, we analysis the loss probability distribution function if default event taken place and achieve the prices based on the results of Vasicek (1987). Under normal condition, we can approximate the price of CDO tranches analytically, but in the other distributions, complete analytical solution is often non-existent, or numerically difficult to achieve, so this is the point where Monte Carlo methods came into use to simulate the price of CDO tranches. We compared the semi-analytical prices derived under the condition of single normal factor with the results reached using Monte Carlo method.As default probability of a single asset is concerned, we derive the credit spreads curve through other credit products based on the same subject in the real market, thus calculate the marginal distribution of default probability. As a matter of fact, this is all set up in the risk neutral probability measure, and belongs to reduced-form Model.We highlight the use of Copula functions to analysis the default correlation between underlying assets. Copula function has a wonderful characteristic; it can not only describe simple linear correlation between assets, but also nonlinear and tail correlations. This adapts to the situation when capital gains are not subject to the normal distribution. Compared to the situation under single normal factor, copula function can make up its defects and capture the non-linear relationship between underlying assets, and also the non-normal, non-symmetric information on the tail. This adds up and weights to the analysis of default correlation between multi-assets.Finally, we base on the latest issued iTraxx Europe index of the synthetic CDO products, select six underlying assets, using their daily log returns as proxy variables, statistically analysis the distribution of the assets and default correlation coefficient between them, and estimate parameters under different model. The final prices of different tranches are simulated by Monte Carlo method. Based on the results we obtained, we analysis the sensitivity of CDO tranches to the default correlations, compare applicability and advantages of different models and methods.In Chapter II of this paper, we discuss the pricing of CDO tranches under non-arbitrage methods, normal single factor method and Monte Carlo method. Chapter III analysis default probability of a single asset under risk-neutral probability measure and compare linear correlation under normal condition with the nonlinear correlation using copula function. Chapter IV we numerically realize the prices of CDO tranches, and analysis the sensitivity based on result obtained. In the final chapter V, in accordance with the discussion and the results before, we sum up the problems existed in the process of CDO pricing and forward the direction of future improvement.