On absolutely continuous compensators and nonlinear filtering equations in default risk models
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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- Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
- Hayne E. Leland., 1994.
"Corporate Debt Value, Bond Covenants, and Optimal Capital Structure,"
Research Program in Finance Working Papers
RPF-233, University of California at Berkeley.
- Leland, Hayne E, 1994. " Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Journal of Finance, American Finance Association, vol. 49(4), pages 1213-52, September.
- 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.
- 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.
- Umut Cetin & R. Jarrow & P. Protter & Y. Yildirim, 2004.
"Modeling credit risk with partial information,"
LSE Research Online Documents on Economics
2840, London School of Economics and Political Science, LSE Library.
- 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.
- 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 123456789/4436, Paris Dauphine University.
- R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195.
- Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
- Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
- P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, 09.
- Rüdiger Frey & Thorsten Schmidt, 2009. "Pricing Corporate Securities Under Noisy Asset Information," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 403-421.
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