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Quadratic Portfolio Credit Risk models with Shot-noise Effects

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Author Info

  • Gaspar, Raquel M.

    ()
    (Dept. of Finance, Stockholm School of Economics)

  • Schmidt, Thorsten

    ()
    (Department of Mathematics, University of Leipzig)

Abstract

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.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 616.

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Length: 60 pages
Date of creation: 02 Dec 2005
Date of revision:
Handle: RePEc:hhs:hastef:0616

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Related research

Keywords: Credit risk; reduced-form models; CDS; CDO; quadratic term structures; shot-noise;

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References

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  1. Gaspar, Raquel M., 2004. "General Quadratic Term Structures of Bond, Futures and Forward Prices," Working Paper Series in Economics and Finance 559, Stockholm School of Economics.
  2. Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997. "A Markov Model for the Term Structure of Credit Risk Spreads," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 481-523.
  3. Damir Filipović, 2002. "Separable Term Structures And The Maximal Degree Problem," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 341-349.
  4. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
  5. Philipp J. Schönbucher, 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers bgse15_2001, University of Bonn, Germany.
  6. 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.
  7. 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.
  8. Gaspar, Raquel M. & Slinko, Irina, 2005. "Correlation Between Intensity and Recovery in Credit Risk Models," Working Paper Series in Economics and Finance 614, Stockholm School of Economics.
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Citations

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Cited by:
  1. Schmidt, Thorsten & Stute, Winfried, 2007. "Shot-noise processes and the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1332-1338, July.
  2. Chernobai, Anna & Yildirim, Yildiray, 2008. "The dynamics of operational loss clustering," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2655-2666, December.
  3. Gaspar, Raquel M. & Slinko, Irina, 2005. "Correlation Between Intensity and Recovery in Credit Risk Models," Working Paper Series in Economics and Finance 614, Stockholm School of Economics.

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