Some Reduced Form Credit Risk Models With Regime Switching

As the environment of modern financial market is increasingly complex,credit risk has become the main risk that many financial institutions need to face.The global financial crisis of 2008 has made people aware of the importance of managing credit risks.In the modern credit risk theory,the reduced form credit risk model has become an important credit risk measurement model,which can better incorporate the default factors into default intensities.The economic activity shows that macroeconomic environment sometimes has a significant impact on credit quality of the obligor.People usually use continuous time Markov chain to describe the change of macroeconomic state.This thesis constructs several kinds of reduced form credit risk models with regime switching,and studies the default dependence structure,default contagion,and the pricing of portfolio credit derivatives and mortgage-backed securities.This thesis makes some innovative works in the following three aspects:Firstly,we propose a conditionally independent reduced form credit risk model with regime switching and study the pricing of several important portfolio credit derivatives.We assume that the default intensities of reference entities are modelled by some dependent regime switching shot-noise processes and the individual jumps of the intensity are driven by a common latent factor.By means of the Markov chain theory and conditional expectation properties,we obtain the Laplace transform of regime switching shot-noise processes,the distribution of default number of reference entities in a given period and the distribution of ordered default times.On this basis,we derive the analytical expressions of the fair spreads of basket credit default swap,collateralized debt obligation and credit default swap index.Some numerical results are also given.Secondly,we study the infectious effect between defaultable firms.We extend the looping default model to a contagion model with regime switching.In this model,the default intensity processes are driven not only by the common macroeconomic factors,but also by the defaults of other considered firms.By changing measure,we derive the conditional joint default probability of the defaultable firms,conditional marginal distribution of the default time and the Laplace transform of the default intensity processes.Furthermore,we obtain the analytical expressions of the fair spreads of the first and the second to default CDSs on two underlyings.Numerical results are presented to show the impacts of the model parameters on the fair spreads.Thirdly,we study the pricing of defaultable mortgage-backed securities influenced by the macroeconomic environment.We first analyze the cash flow of mortgage loan,and give the value process of mortgage loan under the influence of the macroeconomic environment.On this basis,we take the mortgage pool as a whole.We introduce a regime switching default process to describe the credit risk of mortgage pool and propose a reduced form credit risk model with regime switching.Combined with the cash flow of mortgage-backed securities,we derive a explicit pricing formula for mortgage-backed securities.Numerical results are presented to show the relationships between the price of mortgage-backed securities and the model parameters.