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

Author

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  • Herbertsson, Alexander

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

  • Rootzén, Holger

    () (Department of Mathematical Statistic)

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.

Suggested Citation

  • Herbertsson, Alexander & Rootzén, Holger, 2007. "Pricing k-th-to-default Swaps under Default Contagion: The Matrix-Analytic Approach," Working Papers in Economics 269, University of Gothenburg, Department of Economics.
  • Handle: RePEc:hhs:gunwpe:0269
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    File URL: http://hdl.handle.net/2077/7463
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    References listed on IDEAS

    as
    1. Duffie, Darrell & Saita, Leandro & Wang, Ke, 2007. "Multi-period corporate default prediction with stochastic covariates," Journal of Financial Economics, Elsevier, vol. 83(3), pages 635-665, March.
    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. Houweling, Patrick & Vorst, Ton, 2005. "Pricing default swaps: Empirical evidence," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1200-1225, December.
    4. 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..
    5. 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, pages 193-226.
    6. 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.
    7. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    8. Giesecke, Kay & Weber, Stefan, 2004. "Cyclical correlations, credit contagion, and portfolio losses," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 3009-3036, December.
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    More about this item

    Keywords

    Portfolio credit risk; intensity-based models; default dependence modelling; default contagion; CDS; kth-to-default swaps; Markov jump processes; Matrix-analytic 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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