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Credit Spread Bounds and their Implications for Credit Risk Modeling

by Ren-Raw Chen of Rutgers University, and
Jing-zhi Huang of Pennsylvania State University

June 20, 2002

Abstract: Analogous to the yield curve which is essential in pricing interest rate contingent claims, the default probability curve is indispensable for pricing credit derivatives. However, when such a curve is generated by calibrating credit models to observed credit spreads, negative default probabilities often occur, which indicates a violation of no arbitrage. In this paper we present a formal treatment of this negative probability problem known in the credit researcher community. Specifically, for a large class of credit models we derive a set of analytical bounds within which a model will be consistent with an observed term structure of credit spreads (in the sense that the model-implied default probabilities are well defined). We also obtain some general results regarding the implications of the shape of the observed credit spread curve on the consistency of a credit risk model. In particular, we identify a class of models that are consistent only when the observed credit spread curves are flat at the long end.

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