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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.

Suggested Citation

  • Didier Rulli`ere & Diana Dorobantu & Areski Cousin, 2009. "An extension of Davis and Lo's contagion model," Papers 0904.1653, arXiv.org, revised Feb 2010.
  • Handle: RePEc:arx:papers:0904.1653
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    References listed on IDEAS

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    1. 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.
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    3. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    4. Fan Yu, 2007. "Correlated Defaults In Intensity-Based Models," Mathematical Finance, Wiley Blackwell, vol. 17(2), pages 155-173.
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    6. 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.
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    8. Philippe Jorion & Gaiyan Zhang, 2010. "Information Transfer Effects of Bond Rating Downgrades," The Financial Review, Eastern Finance Association, vol. 45(3), pages 683-706, August.
    9. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515 World Scientific Publishing Co. Pte. Ltd..
    10. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    11. Boissay, Frédéric, 2006. "Credit chains and the propagation of financial distress," Working Paper Series 573, European Central Bank.
    12. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    13. Jorion, Philippe & Zhang, Gaiyan, 2007. "Good and bad credit contagion: Evidence from credit default swaps," Journal of Financial Economics, Elsevier, vol. 84(3), pages 860-883, June.
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    Cited by:

    1. 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.
    2. Gagliardini, Patrick & Gouriéroux, Christian, 2013. "Correlated risks vs contagion in stochastic transition models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(11), pages 2241-2269.

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