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Pricing k-th-to-default Swaps under Default Contagion: The Matrix-Analytic Approach

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  • Herbertsson, Alexander

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

  • Rootzén, Holger

    ()
    (Department of Mathematical Statistic)

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    Abstract

    We study a model for default contagion in intensity-based credit risk and its consequences for pricing portfolio credit derivatives. The model is specified through default intensities which are assumed to be constant between defaults, but which can jump at the times of defaults. The model is translated into a Markov jump process which represents the default status in the credit portfolio. This makes it possible to use matrix-analytic methods to derive computationally tractable closed-form expressions for single-name credit default swap spreads and kth-to-default swap spreads. We ”semicalibrate” the model for portfolios (of up to 15 obligors) against market CDS spreads and compute the corresponding kth-to-default spreads. In a numerical study based on a synthetic portfolio of 15 telecom bonds we study a number of questions: how spreads depend on the amount of default interaction; how the values of the underlying market CDS-prices used for calibration influence kth-th-to default spreads; how a portfolio with inhomogeneous recovery rates compares with a portfolio which satisfies the standard assumption of identical recovery rates; and, finally, how well kth-th-to default spreads in a nonsymmetric portfolio can be approximated by spreads in a symmetric portfolio.

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    File URL: http://hdl.handle.net/2077/7463
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    Bibliographic Info

    Paper provided by University of Gothenburg, Department of Economics in its series Working Papers in Economics with number 269.

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    Length: 28 pages
    Date of creation: 31 Oct 2007
    Date of revision:
    Handle: RePEc:hhs:gunwpe:0269

    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; default dependence modelling; default contagion; CDS; kth-to-default swaps; Markov jump processes; Matrix-analytic methods;

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    References

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    1. Darrel Duffie & Leandro Saita & Ke Wang, 2005. "Multi-Period Corporate Default Prediction With Stochastic Covariates," CARF F-Series CARF-F-047, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
    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. Houweling, P. & Vorst, A.C.F., 2003. "Pricing default swaps: empirical evidence," Econometric Institute Research Papers EI 2003-51, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    5. 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.
    6. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    7. Giesecke, Kay & Weber, Stefan, 2006. "Credit contagion and aggregate losses," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 741-767, May.
    8. 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.
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