Risk Analysis And Applications Of A Class Of Reduced Credit Risk Models

Since the2007subprime crisis, a quantitative analysis of default risk has beenattracting a lot of attention. The class of reduced form models is a very important classof credit risk models, and the modeling of the default dependence structure is essentialin the reduced form models. In this dissertation, we study the modeling of defaultdependence structure in the reduced form framework, and make a quantitative analysisof default risk. We price the most fundamental products in the credit derivativesmarket.So far, there are four major approaches generating default dependence withinthe reduced form framework: the interacting intensities models, the copula models,the conditionally independent default models, and the common shock models. Thisdissertation proposes a thinning-dependent structure model and a Markov copula modelwith regime switching, which have a close relationship with the common shock model.We make a quantitative analysis of default risk, that is we investigate the joint defaultprobabilities under the proposed models. In the end of the dissertation, we study thepricing problem of the credit derivatives.The thinning-dependent structure credit risk model becomes the common shockmodel, when the thinning probabilities are set to be special values. So we can saythat the thinning-dependent structure model is a generalization of the common shockmodel. We introduce an economic state variable in this model, which is described by aMarkov chain. Thus we propose a reduced model with thinning dependence structureamong default intensity processes with regime switching. First, we consider a simplecase: intensity processes take diferent constant values with the change of the economicstatus, and then consider the case that the intensity process is a jump-difusion process,with the drift coefcients and difusion coefcients take diferent constant values withthe change of the economic status. And then we make the quantitative analysis of default risk in the models. The pricing formulas of portfolio credit derivatives, such asbasket default swaps, CDX, CDO, are also provided.Similarly to the common shock model, the default dependence comes from si-multaneous defaults in the Markov copula model. But it pays more attention to thecharacterization of default events in the common shock model, while it pays moreattention to the characterization of default indicator processes in the Markov copulamodel. So the quantitative analysis of default risk in the two models are diferent, andit uses the martingale approach in the Markov copula model.In this dissertation, we apply the Markov chain copula model to the pricing ofCDS with bilateral counterparty risk, and then perform some numerical experimentsto analyze the diference of the fair spreads between the unilateral case and the bilateralcase.Furthermore, we introduce an economic state variable in the Markov copula model,such that the default correlation is generated by the simultaneous default factors andeconomic environment factors. We prove that the default indicator processes in thenew model still have martingale property. In this proposed model, a pricing formula ofCDS with bilateral counterparty risk is derived. In the end, we perform some numericalexperiments to analyze the impact of the economic environment on the fair spreads.