  In this paper we consider a reduced-form intensity-based credit risk model
with a hidden Markov state process. A filtering method is proposed for
extracting the underlying state given the observation processes. The method may
be applied to a wide range of problems. Based on this model, we derive the
joint distribution of multiple default times without imposing stringent
assumptions on the form of default intensities. Closed-form formulas for the
distribution of default times are obtained which are then applied to solve a
number of practical problems such as hedging and pricing credit derivatives.
The method and numerical algorithms presented may be applicable to various
forms of default intensities.
