Modelling Contagion Effect Of Credit Risk And Pricing Of Credit Derivatives

Credit risk as the risk that an obligator may default on its contractual payment obligations, is a complicated issue for financial institutions especially for banking sectors. After some financial crises such as Asian financial crisis, the contagion effect of credit risk has attracted huge attention of financial market regulators and financial institutions. Using credit derivatives to transfer, elude and hedge credit risk has become more and more common, which requires fair valuation of credit derivatives and the occurrence of US Subprime Mortgage Crisis is an example. This thesis concentrates on modeling contagion effect of couterparty risk and valuation of defaultable risky bonds and the credit derivatives. Specifically, the present study is conducted from the following five perspectives.Firstly, a hyperbolic function is introduced in Jarrow & Yu model to reflect the attenuating contagion effect of one firm's default on its partner. If two firms have strong bussiness relationship, one firm's default intensity will jump when there is an occurrence of default event of the other firm. This phenomenon is called contagion effect. The infected firm will As time goes on, the contagion effect will decrease gradually until extincts. This attenuating process is expressed by the hyperbolic function. By employing change of measure, the joint distribution and marginal distributions of default times are derived. Thus the fair prices of defaultable risky bonds and credit default swaps (CDS) can be valued.Secondly, the hyperbolic attenuation function is generalized to a general non-negative and decreasing function. Accordingly, the joint distribution and marginal distributions of default times are derived. Thus we can value the fair prices of defaultable risky bonds and credit default swaps (CDS).Thirdly, the thesis takes into account the dynamic duration of contagion effect. A random variable is introduced to denote an uncertain period of time, reflecting how long the contagion effect of one firm's default on its partner's default intensity. In this model, one firm's default event may cause other firm's default intensity a jump, due to their close economic linkage. After a random period, the contagion effect will disappear. By employing change of measure, the general joint distribution and marginal distributions of default times are derived. Then the closed formulae of prices risky bonds and some credit derivatives such as CDS and collateralized bond obligation (CBO) are obtained.Fourthly, we consider dynamicly attenuating contagion effect of counterparty risk by introducing random variables together with attenuation functions in firm's intensity processes. In this model, one firm's default has contagion effect, triggering a jump in the survival firms' default intensities. Then the default's contagion effect will decrease, the weakening process denoted by the attenuation function. After a random period, the impact will disappear. By employing change of measure, the general joint distribution and marginal distributions of default times are derived and the risky bond and the credit derivatives such as CDS can be valued. From the explicit pricing formula of CDS, we can clearly interpret how the couterparty risk effects the swap premium.At last, we investigates the effects of interest rate risk and the counterparty risk on the intensity process in the reduced framework. A formula for valuing risky bond is derived.In brief, this dissertation presents some more realistic models to reflect contagion effect of counterparty risk. By employing change of measure, the general joint distribution and marginal distributions of default times are derived. So the risky bonds and some credit derivatives such as CDS and CBO can be valued. From the explicit pricing formula of CDS, how the couterparty risk effects the swap premium can be clearly interpreted. This dissertation offers some theoretical backgrounds and empirical evidences for financial innovation.