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.