A General Formula for Valuing Defaultable Securities
Abstract
Previous research 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 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. Copyright The Econometric Society 2004.Download Info
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Bibliographic Info
Article provided by Econometric Society in its journal Econometrica.
Volume (Year): 72 (2004)
Issue (Month): 5 (09)
Pages: 1377-1407
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Handle: RePEc:ecm:emetrp:v:72:y:2004:i:5:p:1377-1407
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Bao, Qunfang & Chen, Si & Liu, Guimei & Li, Shenghong, 2010. "Unilateral CVA for CDS in Contagion model: With volatilities and correlation of spread and interest," MPRA Paper 28250, University Library of Munich, Germany, revised 27 Dec 2010.
- repec:cdl:ucsdec:128083 is not listed on IDEAS
- Rosenthal, Dale W.R., 2012. "Approximating correlated defaults," MPRA Paper 36788, University Library of Munich, Germany.
- Bao, Qunfang & Li, Shenghong & Liu, Guimei, 2010.
"Survival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing
[Survival measures and interacting intensity model: with applications in guaranteed debt pricing]," MPRA Paper 27698, University Library of Munich, Germany, revised 27 Dec 2010. - Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007.
"Common Failings: How Corporate Defaults Are Correlated,"
Journal of Finance,
American Finance Association, vol. 62(1), pages 93-117, 02.
- Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006. "Common Failings: How Corporate Defaults are Correlated," NBER Working Papers 11961, National Bureau of Economic Research, Inc.
- Eric Wong & Cho-Hoi Hui, 2009. "A Liquidity Risk Stress-Testing Framework with Interaction between Market and Credit Risks," Working Papers 0906, Hong Kong Monetary Authority.
- Alexander Herbertsson, 2011. "Modelling default contagion using multivariate phase-type distributions," Review of Derivatives Research, Springer, vol. 14(1), pages 1-36, April.
- Muendler, Marc-Andreas, 2005. "Risk Neutral Investors Do Not Acquire Information¤," University of California at San Diego, Economics Working Paper Series qt8fg5g853, Department of Economics, UC San Diego.
- Frank Zhang, 2010. "An empirical analysis of alternative recovery risk models and implied recovery rates," Review of Derivatives Research, Springer, vol. 13(2), pages 101-124, July.
- Bao, Qunfang & Chen, Si & Liu, Guimei & Li, Shenghong, 2010. "Unilateral CVA for CDS in contagion model: with volatilities and correlation of spread and interest," MPRA Paper 26277, University Library of Munich, Germany, revised 27 Dec 2010.
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