Quadratic Portfolio Credit Risk models with Shot-noise Effects
We propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds. Further on, we study a model for portfolio credit risk where we consider both firm specific and systematic risks. The model generalizes the attempt from Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering of defaults. Then, we show how to price first-to-default swaps, CDOs, and draw the link to currently proposed credit indices.
|Date of creation:||02 Dec 2005|
|Date of revision:|
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- Gaspar, Raquel M. & Slinko, Irina, 2005. "Correlation Between Intensity and Recovery in Credit Risk Models," SSE/EFI Working Paper Series in Economics and Finance 614, Stockholm School of Economics.
- Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008.
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World Scientific Book Chapters,
in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453
World Scientific Publishing Co. Pte. Ltd..
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- Leippold, Markus & Wu, Liuren, 2002.
"Asset Pricing under the Quadratic Class,"
Journal of Financial and Quantitative Analysis,
Cambridge University Press, vol. 37(02), pages 271-295, June.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999.
"Transform Analysis and Asset Pricing for Affine Jump-Diffusions,"
NBER Working Papers
7105, National Bureau of Economic Research, Inc.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
- Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," SSE/EFI Working Paper Series in Economics and Finance 559, Stockholm School of Economics.
- Philipp J. Schönbucher, 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers bgse15_2001, University of Bonn, Germany.
- Damir Filipović, 2002. "Separable Term Structures And The Maximal Degree Problem," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 341-349.
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