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An extension of Davis and Lo's contagion model

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  • Didier Rulli\`ere

    (SAF)

  • Diana Dorobantu

    (SAF)

  • Areski Cousin

    (SAF)

Abstract

The present paper provides a multi-period contagion model in the credit risk field. Our model is an extension of Davis and Lo's infectious default model. We consider an economy of n firms which may default directly or may be infected by other defaulting firms (a domino effect being also possible). The spontaneous default without external influence and the infections are described by not necessarily independent Bernoulli-type random variables. Moreover, several contaminations could be required to infect another firm. In this paper we compute the probability distribution function of the total number of defaults in a dependency context. We also give a simple recursive algorithm to compute this distribution in an exchangeability context. Numerical applications illustrate the impact of exchangeability among direct defaults and among contaminations, on different indicators calculated from the law of the total number of defaults. We then examine the calibration of the model on iTraxx data before and during the crisis. The dynamic feature together with the contagion effect seem to have a significant impact on the model performance, especially during the recent distressed period.

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Paper provided by arXiv.org in its series Papers with number 0904.1653.

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Date of creation: Apr 2009
Date of revision: Feb 2010
Handle: RePEc:arx:papers:0904.1653

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  1. Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006. "Common Failings: How Corporate Defaults are Correlated," NBER Working Papers 11961, National Bureau of Economic Research, Inc.
  2. Robert A. Jarrow, 2001. "Counterparty Risk and the Pricing of Defaultable Securities," Journal of Finance, American Finance Association, American Finance Association, vol. 56(5), pages 1765-1799, October.
  3. Jorion, Philippe & Zhang, Gaiyan, 2007. "Good and bad credit contagion: Evidence from credit default swaps," Journal of Financial Economics, Elsevier, Elsevier, vol. 84(3), pages 860-883, June.
  4. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
  5. Herbertsson, Alexander, 2007. "Pricing Synthetic CDO Tranches in a Model with Default Contagion Using the Matrix-Analytic Approach," Working Papers in Economics 270, University of Gothenburg, Department of Economics.
  6. Boissay, Frédéric, 2006. "Credit chains and the propagation of financial distress," Working Paper Series, European Central Bank 0573, European Central Bank.
  7. M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 1(4), pages 382-387.
  8. Friedel Epple & Sam Morgan & Lutz Schloegl, 2007. "Joint Distributions Of Portfolio Losses And Exotic Portfolio Products," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 733-748.
  9. Egloff, Daniel & Leippold, Markus & Vanini, Paolo, 2007. "A simple model of credit contagion," Journal of Banking & Finance, Elsevier, Elsevier, vol. 31(8), pages 2475-2492, August.
  10. Rüdiger Frey & Jochen Backhaus, 2008. "Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
  11. Denuit, Michel & Lefevre, Claude & Utev, Sergey, 2002. "Measuring the impact of dependence between claims occurrences," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 1-19, February.
  12. Philippe Jorion & Gaiyan Zhang, 2010. "Information Transfer Effects of Bond Rating Downgrades," The Financial Review, Eastern Finance Association, Eastern Finance Association, vol. 45(3), pages 683-706, 08.
  13. Denuit, Michel & Dhaene, Jan & Ribas, Carmen, 2001. "Does positive dependence between individual risks increase stop-loss premiums?," Insurance: Mathematics and Economics, Elsevier, vol. 28(3), pages 305-308, June.
  14. Fan Yu, 2007. "Correlated Defaults In Intensity-Based Models," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 17(2), pages 155-173.
  15. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, Elsevier, vol. 28(12), pages 3009-3036, December.
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Cited by:
  1. Gagliardini, Patrick & Gouriéroux, Christian, 2013. "Correlated risks vs contagion in stochastic transition models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 37(11), pages 2241-2269.
  2. Patrick Gagliardini & Christian Gouriéroux, 2012. "Correlated Risks vs Contagion in Stochastic Transition Models," Working Papers, Centre de Recherche en Economie et Statistique 2012-07, Centre de Recherche en Economie et Statistique.
  3. Stéphane Loisel & Pierre Arnal & Romain Durand, 2010. "Correlation crises in insurance and finance, and the need for dynamic risk maps in ORSA," Working Papers hal-00502848, HAL.

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