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Modelling Default Contagion Using Multivariate Phase-Type Distributions

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  • Herbertsson, Alexander

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    (Department of Economics, School of Business, Economics and Law, Göteborg University)

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    Abstract

    We model dynamic credit portfolio dependence by using default contagion in an intensity-based framework. Two different portfolios (with 10 obligors), one in the European auto sector, the other in the European financial sector, are calibrated against their market CDS spreads and the corresponding CDS-correlations. After the calibration, which are perfect for the banking portfolio, and good for the auto case, we study several quantities of importance in active credit portfolio management. For example, implied multivariate default and survival distributions, multivariate conditional survival distributions, implied default correlations, expected default times and expected ordered defaults times. The default contagion is modelled by letting individual intensities jump when other defaults occur, but be constant between defaults. This model is translated into a Markov jump process, a so called multivariate phase-type distribution, which represents the default status in the credit portfolio. Matrix-analytic methods are then used to derive expressions for the quantities studied in the calibrated portfolios.

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    File URL: http://hdl.handle.net/2077/7465
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    Bibliographic Info

    Paper provided by University of Gothenburg, Department of Economics in its series Working Papers in Economics with number 271.

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    Length: 36 pages
    Date of creation: 31 Oct 2007
    Date of revision:
    Handle: RePEc:hhs:gunwpe:0271

    Contact details of provider:
    Postal: Department of Economics, School of Business, Economics and Law, University of Gothenburg, Box 640, SE 405 30 GÖTEBORG, Sweden
    Phone: 031-773 10 00
    Web page: http://www.handels.gu.se/econ/
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    Related research

    Keywords: Portfolio credit risk; intensity-based models; dynamic dependence modelling; CDS-correlation; default contagion; Markov jump processes; multivariate phase-type distributions; matrixanalytic methods;

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    1. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    2. Giesecke, Kay & Weber, Stefan, 2006. "Credit contagion and aggregate losses," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 741-767, May.
    3. Søren Asmussen, 2000. "Matrix-analytic Models and their Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 27(2), pages 193-226.
    4. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    5. M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 382-387.
    6. Robert A. Jarrow, 2001. "Counterparty Risk and the Pricing of Defaultable Securities," Journal of Finance, American Finance Association, vol. 56(5), pages 1765-1799, October.
    7. 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.
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