A General Formula for Valuing Defaultable Securities

Carnegie Mellon Department of Finance Working Paper

26 Pages Posted: 17 Feb 2003

See all articles by Pierre Collin-Dufresne

Pierre Collin-Dufresne

Ecole Polytechnique Fédérale de Lausanne; Swiss Finance Institute; National Bureau of Economic Research (NBER)

Robert S. Goldstein

University of Minnesota - Twin Cities - Carlson School of Management; National Bureau of Economic Research (NBER)

Julien Hugonnier

École Polytechnique Fédérale de Lausanne; Centre for Economic Policy Research (CEPR)

Date Written: January 2003

Abstract

Previous research (e.g., Lando (1998), Duffie, Schroder and Skiadas (1996), Duffie and Singleton (1999)) has shown that under a suitable no-jump condition, the price of a defaultable security is equal to its risk-neutral expected discounted cash flows if a modified discount rate is introduced to account for the possibility of default. Below, we generalize this result by demonstrating that one can always (i.e., even when the no-jump condition is violated) value defaultable claims using expected risk-adjusted discounting provided that the expectation is taken under a slightly modified probability measure. This new probability measure puts zero probability on paths where default occurs prior to the maturity, and is thus only absolutely continuous with respect to the risk-neutral probability measure. After establishing the general result and discussing its relation with the existing literature, we investigate several examples for which the no-jump condition fails. Each example illustrates the power of our general formula by providing simple analytic solutions for the prices of defaultable securities.

Keywords: reduced-form models of default, Cox Processes

JEL Classification: G13

Suggested Citation

Collin-Dufresne, Pierre and Goldstein, Robert S. and Hugonnier, Julien, A General Formula for Valuing Defaultable Securities (January 2003). Carnegie Mellon Department of Finance Working Paper, Available at SSRN: https://ssrn.com/abstract=368700 or http://dx.doi.org/10.2139/ssrn.368700

Pierre Collin-Dufresne (Contact Author)

Ecole Polytechnique Fédérale de Lausanne ( email )

Quartier UNIL-Dorigny, Bâtiment Extranef, # 211
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Swiss Finance Institute

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National Bureau of Economic Research (NBER)

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Robert S. Goldstein

University of Minnesota - Twin Cities - Carlson School of Management ( email )

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National Bureau of Economic Research (NBER)

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Cambridge, MA 02138
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Julien Hugonnier

École Polytechnique Fédérale de Lausanne ( email )

Quartier UNIL Dorigny
Extranef
Lausanne, CH-1015
Switzerland

HOME PAGE: http://https://www.epfl.ch/labs/sfi-jh/

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

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