Jumps in intensity models: investigating the performance of Ornstein-Uhlenbeck processes in credit risk modeling

摘要

This work presents intensity-based credit risk models where the default intensity of the point process is modeled by an Ornstein-Uhlenbeck type process completely driven by jumps. Under this model we compute the default probability over time by linking it to the characteristic function of the integrated intensity process. In case of the Gamma and the Inverse Gaussian Ornstein-Uhlenbeck processes this leads to a closed-form expression for the default probability and to a straightforward estimate of credit default swaps prices. The model is calibrated to a series of real-market term structures and then used to price a digital default put option. Results are compared with the well known cases of Poisson and CIR dynamics. Possible extensions of the model to the multivariate setting are finally discussed. Keywords Ornstein-Uhlenbeck process - Credit risk - Survival probability - Intensity-based model - Credit default swap