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A General Framework for Pricing Credit Risk

by Alain Bélanger of Scotia Capital,
Steven E. Shreve of Carnegie Mellon University, and
Dennis Wong of Bank of America Corporation

April 16, 2003

Abstract: A framework is provided for pricing derivatives on defaultable bonds and other credit-risky contingent claims. The framework is in the spirit of reduced form models, but extends these models to include the case that default can occur only at specific times, such as coupon payment dates. While the framework does not provide an efficient setting for obtaining results about structural models, it is sufficiently general to include most structural models, and thereby highlights the commonality between reduced-form and structural models. Within the general framework, multiple recovery conventions for contingent claims are considered: recovery of a fraction of par, recovery of a fraction of a no-default version of the same claim, and recovery of a fraction of the pre-default value of the claim. A stochastic-integral representation for credit-risky contingent claims is provided, and the integrand for the credit exposure part of this representation is identified. In the case of intensity-based reduced-form models, credit spread and credit risky term structure are studied.

JEL Classification: G13.

AMS Classification: 90A09, 60H30, 60G44.

Keywords: credit risk, credit derivatives, reduced-form models, structural models.

Published in: Mathematical Finance, Vol. 14, No. 3,  (July 2004), pp. 317-350.

Previously titled: A Unified Model for Credit Derivatives

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