A reduced-form model with default intensities containing contagion and regime-switching Vasicek processes

The contagion credit risk model is used to describe the contagion effect among different financial institutions. Under such a model, the default intensities are driven not only by the common risk factors, but also by the defaults of other considered firms. In this paper, we consider a two-dimensional credit risk model with contagion and regime-switching. We assume that the default intensity of one firm will jump when the other firm defaults and that the intensity is controlled by a Vasicek model with the coefficients allowed to switch in different regimes before the default of other firm. By changing measure, we derive the marginal distributions and the joint distribution for default times. We obtain some closed form results for pricing the fair spreads of the first and the second to default credit default swaps (CDSs). Numerical results are presented to show the impacts of the model parameters on the fair spreads.