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

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  • Umut c{C}etin

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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  • Umut c{C}etin, 2012. "On absolutely continuous compensators and nonlinear filtering equations in default risk models," Papers 1205.1154, arXiv.org.
    • Handle: RePEc:arx:papers:1205.1154
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    References listed on IDEAS

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    1. 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, vol. 11(4), pages 591-602, October.
    2. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-664, May.
    3. Leland, Hayne E, 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-1252, September.
    4. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409, World Scientific Publishing Co. Pte. Ltd..
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    6. Delia Coculescu & Hélyette Geman & Monique Jeanblanc, 2008. "Valuation of default-sensitive claims under imperfect information," Finance and Stochastics, Springer, vol. 12(2), pages 195-218, April.
    7. Rüdiger Frey & Wolfgang Runggaldier, 2010. "Pricing credit derivatives under incomplete information: a nonlinear-filtering approach," Finance and Stochastics, Springer, vol. 14(4), pages 495-526, December.
    8. Rüdiger Frey & Thorsten Schmidt, 2009. "Pricing Corporate Securities Under Noisy Asset Information," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 403-421, July.
    9. Umut Çetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2008. "Modeling Credit Risk With Partial Information," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 23, pages 579-590, World Scientific Publishing Co. Pte. Ltd..
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    11. repec:dau:papers:123456789/4436 is not listed on IDEAS
    12. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    13. Robert Jarrow & Philip Protter & A. Sezer, 2007. "Information reduction via level crossings in a credit risk model," Finance and Stochastics, Springer, vol. 11(2), pages 195-212, April.
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