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Credit Risk with asymmetric information on the default threshold

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Author Info

  • Caroline Hillairet

    ()
    (CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique - Polytechnique - X - CNRS : UMR7641)

  • Ying Jiao

    ()
    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Paris VI - Pierre et Marie Curie - Université Paris VII - Paris Diderot)

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    Abstract

    We study the impact of asymmetric information in a general credit model where the default is triggered when a fundamental diff usion process of the firm passes below a random threshold. Inspired by some recent technical default events during the fi nancial crisis, we consider the role of the firm's managers who choose the level of the default threshold and have complete information. However, other investors on the market only have partial observations either on the process or on the threshold. We specify the accessible information for di fferent types of investors. Besides the framework of progressive enlargement of fi ltrations usually adopted in the credit risk modelling, we also combine the results on initial enlargement of filtrations to deal with the uncertainty on the default threshold. We consider several types of investors who have di fferent information levels and we compute the default probabilities in each case. Numerical illustrations show that the insiders who have extra information on the default threshold obtain better estimations of the default probability compared to the standard market investors.

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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number hal-00663136.

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    Date of creation: 2012
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    Publication status: Published, Stochastics An International Journal of Probability and Stochastic Processes, 2012, DOI:10.1080/17442508.2011.575944
    Handle: RePEc:hal:journl:hal-00663136

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00663136
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    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords: credit risk; insider; enlargement of filtration;

    References

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    1. Jeanblanc, Monique & Geman, Hélyette & Coculescu, Délia, 2006. "Valuation of default sensitive claims under imperfect information," Economics Papers from University Paris Dauphine 123456789/2191, Paris Dauphine University.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
    3. Monique Jeanblanc & Stoyan Valchev, 2005. "Partial Information And Hazard Process," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 807-838.
    4. Umut Cetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2004. "Modeling Credit Risk with Partial Information," Papers math/0407060, arXiv.org.
    5. Giesecke, Kay, 2006. "Default and information," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2281-2303, November.
    6. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195.
    7. José Corcuera & Peter Imkeller & Arturo Kohatsu-Higa & David Nualart, 2004. "Additional utility of insiders with imperfect dynamical information," Finance and Stochastics, Springer, vol. 8(3), pages 437-450, 08.
    8. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
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