Infinite Dimensional Models for Credit and Mortgage Risk

This talks considers a generalization of the CIR model to infinite dimensions and considers its applications to Credit and Mortgage Risk. First, we discuss the existence of solutions in several Hilbert spaces which leads to stochastic processes which are positive. Second, we use this results to construct a model for credit spreads which is proven to be free of arbitrage. Third, we consider models for Mortgage Risk where the default intensity of an obligor depends on the location. The generalized CIR model will be used to model the intensity. In simulation results we show that wavelet methods can be successfully used to infer the default intensity from data.