Modeling Credit Risk with Partial Information

by Umut Çetin of Cornell University,
Robert Jarrow of Cornell University,
Philip Protter of Cornell University, and
Yıldıray Yıldırım of Syracuse University

August 2004

Abstract: This paper provides an alternative approach to Duffie and Lando [Econometrica 69 (2001) 633-664] for obtaining a reduced form credit risk model from a structural model. Duffie and Lando obtain a reduced form model by constructing an economy where the market sees the manager's information set plus noise. The noise makes default a surprise to the market. In contrast, we obtain a reduced form model by constructing an economy where the market sees a reduction of the manager's information set. The reduced information makes default a surprise to the market. We provide an explicit formula for the default intensity based on an Azéma martingale, and we use excursion theory of Brownian motions to price risky debt.

AMS Classification: 60H60, 60G46, 91B28.

Keywords: Default risk, Azéma martingale, Brownian excursions, default distribution.

Published in: Annals of Applied Probability, Vol. 14, No. 3, (August 2004), pp. 1167-1178.

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