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Pricing Synthetic CDO Tranches in a Model with Default Contagion Using the Matrix-Analytic Approach

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  • Herbertsson, Alexander

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

Abstract

We value synthetic CDO tranche spreads, index CDS spreads, kth-to-default swap spreads and tranchelets in an intensity-based credit risk model with default contagion. The default dependence is modelled by letting individual intensities jump when other defaults occur. The model is reinterpreted as a Markov jump process. This allow us to use a matrix-analytic approach to derive computationally tractable closed-form expressions for the credit derivatives that we want to study. Special attention is given to homogenous portfolios. For a fixed maturity of five years, such a portfolio is calibrated against CDO tranche spreads, index CDS spread and the average CDS and FtD spreads, all taken from the iTraxx Europe series. After the calibration, which render perfect fits, we compute spreads for tranchelets and kth-to-default swap spreads for different subportfolios of the main portfolio. We also investigate implied tranche-losses and the implied loss distribution in the calibrated portfolios.

Suggested Citation

  • 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.
    • Handle: RePEc:hhs:gunwpe:0270
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    File URL: http://hdl.handle.net/2077/7464
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    References listed on IDEAS

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    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. Marco Avellaneda & Lixin Wu, 2001. "Credit Contagion: Pricing Cross-Country Risk In Brady Debt Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(06), pages 921-938.
    3. Herbertsson, Alexander, 2007. "Modelling Default Contagion Using Multivariate Phase-Type Distributions," Working Papers in Economics 271, University of Gothenburg, Department of Economics.
    4. 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.
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    7. 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..
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    Cited by:

    1. Rüdiger Frey & Jochen Backhaus, 2008. "Pricing And Hedging Of Portfolio Credit Derivatives With Interacting Default Intensities," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 611-634.
    2. Herbertsson, Alexander, 2007. "Modelling Default Contagion Using Multivariate Phase-Type Distributions," Working Papers in Economics 271, University of Gothenburg, Department of Economics.
    3. Areski Cousin & Diana Dorobantu & Didier Rullière, 2013. "An extension of Davis and Lo's contagion model," Quantitative Finance, Taylor & Francis Journals, vol. 13(3), pages 407-420, February.
    4. 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.

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    More about this item

    Keywords

    Credit risk; intensity-based models; CDO tranches; index CDS; kth-to-default swaps; dependence modelling; default contagion; Markov jump processes; Matrix-analytic methods;
    All these keywords.

    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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