Pricing Credit Securities In The Contagious Model

Credit derivatives were the financial assets derived from the loan, the bond or other assetsin 1990s. They separated the credit risk from market risk and made the credit risk be tradeableand manageable. The traditional management mode was changed. The financial crisis in thelast century and the occurrence of American subprime mortgage crisis further showed that thecontagious risk was important for transferring and reorganizing the credit risk. Therefore, weneed the fair valuation of credit derivatives and make the theory more helpful. The study on theirpricing is fundamental. This thesis focuses on the pricing of bonds and credit default swaps withcounterparty risk and the pricing of Collateralized Debt Obligations with heterogeneous portfolio.We study the pricing of bonds and credit default swaps from two aspects. One is that thedefaults of the assets depend on the short interest rate or not and the other is that we considerthe pricing respectively in the primary-secondary framework and looping default framework. Thefirst two chapters introduce the setting and notions of credit derivatives, the three correlated modeland three methods of computing the joint distribution of default times in the contagious model.Chapter 3 introduces the short interest rate and the forward interest rate in details. We take moreimportance on three types of the short interest rate: Vasicek model, CIR model and Hull-Whitemodel which are used in the following chapters. Chapter 4 and Chapter 5 discuss the pricing ofbonds and CDS from the two aspects above and give their explicit prices. Chapter 6 consider thepricing of CDO with heterogeneous portfolio and give an example. In this paper, we obtain somenew results by the intensity-based approach of default event as following: In this thesis, the mainresults are obtained with .Firstly, we extend the models in Jarrow and Yu (2001). They proposed the counterparty riskwhich was different from the traditional intensity-based model and solved the problems ignoredby the traditionally structural model and reduced-form model. They introduced primary-secondarymodel and priced bonds and CDS with Vasicek interest rate. We extend their models and considerother interest rate following diffusion processes. On the one hand, we price bonds and CDS whenthe defaults of firms are independent of the default-free term structure. On the other hand, wederive the prices of bonds and CDS when the defaults of firms depend on the default-free termstructure.Secondly, we extend the models in Bai, Hu and Ye (2007). They firstly introduced the conta- gious model with attenuation effect. We price bonds and CDS respectively in primary-secondarymodel and looping default model. Bai, Hu and Ye (2007,2008) only considered the interest rate asa constant and the Vasicek diffusion process. We discuss the other diffusion processes. By usingthe methods in Park (2008), we obtain some important differential equations on the interest rateand price bonds and CDS with a hyperbolic attenuation effect.Thirdly, we further generalize the above models and is extended by adding a hyperbolic at-tenuation effect. We consider the interest rate satisfying jump-diffusion process and obtain somenew results. Moreover, We obtain one explicit solution for bonds and CDS in the similar modelabove. Meanwhile, we make use of Matlab and Monte-Carlos simulation to get the price curves oftheir.At last, we study the contagious model of pricing CDO with heterogeneous portfolio. Thekey of pricing CDO is to valuate the credit risk of the reference assets. Until now, many results arebased on the homogeneous assumption, such as the conditionally independent model and Copulamodel. In this thesis, we apply the hyperbolic attenuation model of two parties in Bai, Hu andYe (2007) to price CDO and obtain the analytic form of CDO tranche's price. In addition, weconsider the contagious model in Zheng and Jiang(2009). They only discussed the pricing of CDSwith many assets. We apply a comparatively simple model to the reference portfolio and obtainthe analytic price of CDO. Moreover, we give the example and the pricing curve of each tranche.