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On absolutely continuous compensators and nonlinear filtering equations in default risk models

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  • Umut \c{C}etin
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    Abstract

    We discuss the pricing of defaultable assets in an incomplete information model where the default time is given by a first hitting time of an unobservable process. We show that in a fairly general Markov setting, the indicator function of the default has an absolutely continuous compensator. Given this compensator we then discuss the optional projection of a class of semimartingales onto the filtration generated by the observation process and the default indicator process. Available formulas for the pricing of defaultable assets are analyzed in this setting and some alternative formulas are suggested.

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    File URL: http://arxiv.org/pdf/1205.1154
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1205.1154.

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    Date of creation: May 2012
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    Handle: RePEc:arx:papers:1205.1154

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    1. Delia Coculescu & Hélyette Geman & Monique Jeanblanc, 2008. "Valuation of default-sensitive claims under imperfect information," Finance and Stochastics, Springer, Springer, vol. 12(2), pages 195-218, April.
    2. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 50(1), pages 53-85, March.
    3. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 10(2), pages 179-195.
    4. Campi, Luciano & Cetin, Umut, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/4436, Paris Dauphine University.
    5. Hayne E. Leland., 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Research Program in Finance Working Papers, University of California at Berkeley RPF-233, University of California at Berkeley.
    6. Umut Cetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2004. "Modeling Credit Risk with Partial Information," Papers math/0407060, arXiv.org.
    7. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    8. Rüdiger Frey & Thorsten Schmidt, 2009. "Pricing Corporate Securities Under Noisy Asset Information," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 19(3), pages 403-421.
    9. Robert Jarrow & Philip Protter & A. Sezer, 2007. "Information reduction via level crossings in a credit risk model," Finance and Stochastics, Springer, Springer, vol. 11(2), pages 195-212, April.
    10. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, Econometric Society, vol. 69(3), pages 633-64, May.
    11. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, Econometric Society, vol. 72(5), pages 1377-1407, 09.
    12. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, Springer, vol. 11(4), pages 591-602, October.
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