Credit Risk Models with Incomplete Information

X. Guo, R. Jarrow, and Y.  Zeng. Credit risk models with incomplete information, (earlier version “Information reduction in credit risk models”,) Mathematics of Operations Research, 34(2): 320-332, 2009.

Abstract: Incomplete information is at the heart of information-based credit risk models. In this paper, we rigorously define incomplete information with the notion of “delayed filtrations”. We characterize two distinct types of delayed information, continuous and discrete: the first
generated by a time change of filtrations and the second by finitely many marked point processes. This notion unifies the noisy information in Duffie and Lando (2001) and the partial information in Collin-Dufresne et al. (2004), under which structural models are translated into reduced-form
intensity-based models. We illustrate through a simple example the importance of this notion of delayed information, as well as the potential pitfall for abusing the Laplacian approximation techniques for calculating the intensity process in an information-based model.