Approximations in Credit Risk Models

In this thesis we present the intensity-based approach to consider default in a general local-stochastic volatility model with stochastic interest rate. In this setting we describe, as in [18], a technique to find approximate solutions of the corresponding partial differential equations and we provide numerical examples in the particular case of JDCEV and Vasicek model, respectively, for the dynamics of the asset and the short rate. Finally, we introduce a formula for the par CDS spreads and applying the approximation method we calibrate our intensity model to credit data finding the model parameters matching the default probabilities implicit in CDS prices (by bootstrapping) to the default probabilities implied by the model itself.