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Modelling Default Contagion Using Multivariate Phase-Type Distributions


  • Herbertsson, Alexander

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


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.

Suggested Citation

  • Herbertsson, Alexander, 2007. "Modelling Default Contagion Using Multivariate Phase-Type Distributions," Working Papers in Economics 271, University of Gothenburg, Department of Economics.
  • Handle: RePEc:hhs:gunwpe:0271

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    References listed on IDEAS

    1. Giesecke, Kay & Weber, Stefan, 2006. "Credit contagion and aggregate losses," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 741-767, May.
    2. M. Davis & V. Lo, 2001. "Infectious defaults," Quantitative Finance, Taylor & Francis Journals, vol. 1(4), pages 382-387.
    3. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
    4. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    5. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    6. 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..
    7. 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.
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    More about this item


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

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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