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A General Formula for Valuing Defaultable Securities

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  • P. Collin-Dufresne
  • R. Goldstein
  • J. Hugonnier
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    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.

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    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2004.00538.x
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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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    Cited by:
    1. Çetin, Umut, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Stochastic Processes and their Applications, Elsevier, vol. 122(11), pages 3619-3647.
    2. 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.
    3. Masaaki Fujii & Akihiko Takahashi, 2011. "Collateralized CDS and Default Dependence -Implications for the Central Clearing-," CARF F-Series CARF-F-246, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    4. Dong, Yinghui & Yuen, Kam C. & Wu, Chongfeng, 2014. "Unilateral counterparty risk valuation of CDS using a regime-switching intensity model," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 25-35.
    5. Rosenthal, Dale W.R., 2008. "Approximating correlated defaults," MPRA Paper 36788, University Library of Munich, Germany, revised 15 Feb 2012.
    6. 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.
    7. Herbertsson, Alexander, 2007. "Modelling Default Contagion Using Multivariate Phase-Type Distributions," Working Papers in Economics 271, University of Gothenburg, Department of Economics.
    8. Alexander Herbertsson, 2011. "Modelling default contagion using multivariate phase-type distributions," Review of Derivatives Research, Springer, vol. 14(1), pages 1-36, April.
    9. Ramaprasad Bhar, 2010. "Stochastic Filtering With Applications In Finance:," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736.
    10. Umut \c{C}etin, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Papers 1205.1154, arXiv.org.
    11. Berndt, Antje & Jarrow, Robert A. & Kang, ChoongOh, 2007. "Restructuring risk in credit default swaps: An empirical analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1724-1749, November.
    12. Herbertsson, Alexander & Rootzén, Holger, 2007. "Pricing k-th-to-default Swaps under Default Contagion: The Matrix-Analytic Approach," Working Papers in Economics 269, University of Gothenburg, Department of Economics.
    13. Masaaki Fujii & Akihiko Takahashi, 2012. "Collateralized CDS and Default Dependence -Implications for the Central Clearing," CARF F-Series CARF-F-281, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    14. Antje Berndt & Peter Ritchken & Zhiqiang Sun, . "On Correlation Effects and Default Clustering in Credit Models," GSIA Working Papers 2008-E36, Carnegie Mellon University, Tepper School of Business.
    15. 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.
    16. Cyril Durand & Marek Rutkowski, 2013. "CVA for Bilateral Counterparty Risk under Alternative Settlement Conventions," Papers 1307.6486, arXiv.org.
    17. Ma, Jin & Yun, Youngyun, 2010. "Correlated intensity, counter party risks, and dependent mortalities," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 337-351, December.
    18. Bao, Qunfang & Li, Shenghong & Liu, Guimei, 2010. "Survival Measures and Interacting Intensity Model: with Applications in Guaranteed Debt Pricing," MPRA Paper 27698, University Library of Munich, Germany, revised 27 Dec 2010.
    19. 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.
    20. Bao, Qunfang & Chen, Si & Li, Shenghong, 2012. "Unilateral CVA for CDS in a contagion model with stochastic pre-intensity and interest," Economic Modelling, Elsevier, vol. 29(2), pages 471-477.
    21. 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.
    22. 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.
    23. Herbertsson, Alexander, 2007. "Pricing Synthetic CDO Tranches in a Model with Default Contagion Using the Matrix-Analytic Approach," Working Papers in Economics 270, University of Gothenburg, Department of Economics.

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