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Credit Risk Models with Incomplete Information

Department of Industrial Engineering and Operations Research, University of California, Berkeley, Berkeley, California 94720
Johnson School of Management, Cornell University, Ithaca, New York 14853, and Kamakura Corporation, Honolulu, Hawaii 96815
Bloomberg R&D, New York, New York 10022
xinguo{at}ieor.berkeley.edu
raj15{at}cornell.edu
yzeng5{at}bloomberg.net

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 [Duffie, D., D. Lando. 2001. Term structures and credit spreads with incomplete accounting information. Econometrica 69 633–664] and the notion of partial information in Collin-Dufresne et al. [Collin-Dufresne, P., R. Goldstein, J. Helwege. 2003. Is credit event risk priced? Modeling contagion via the updating of beliefs. Working paper, Carnegie Mellon University, Pittsburgh], 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.

Key Words: incomplete information; credit risk; delayed filtration; marked point processes
History: Received: January 23, 2007; revision received: June 20, 2008;