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A New Framework For Dynamic Credit Portfolio Loss Modelling

Author

Listed:
  • JAKOB SIDENIUS

    (JP Morgan Securities Ltd., 125 London Wall, London, EC2Y 5AJ, UK)

  • VLADIMIR PITERBARG

    (Barclays Capital, 5 The North Colonnade, London, W1U 6BX, UK)

  • LEIF ANDERSEN

    (Bank of America Securities, 9 West 57th Street, New York, NY 10019, USA)

Abstract

We present the SPA framework, a novel approach to the modeling of the dynamics of portfolio default losses. In this framework, models are specified by a two-layer process. The first layer models the dynamics of portfolio loss distributions in the absence of information about default times. This background process can be explicitly calibrated to the full grid of marginal loss distributions as implied by initial CDO tranche values indexed on maturity, as well as to the prices of suitable options. We give sufficient conditions for consistent dynamics. The second layer models the loss process itself as a Markov process conditioned on the path taken by the background process. The choice of loss process is non-unique. We present a number of choices, and discuss their advantages and disadvantages. Several concrete model examples are given, and valuation in the new framework is described in detail. Among the specific securities for which algorithms are presented are CDO tranche options and leveraged super-senior tranches.

Suggested Citation

  • Jakob Sidenius & Vladimir Piterbarg & Leif Andersen, 2008. "A New Framework For Dynamic Credit Portfolio Loss Modelling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 163-197.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:02:n:s0219024908004762
    DOI: 10.1142/S0219024908004762
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    References listed on IDEAS

    as
    1. Philippe Ehlers & Philipp Schönbucher, 2009. "Background filtrations and canonical loss processes for top-down models of portfolio credit risk," Finance and Stochastics, Springer, vol. 13(1), pages 79-103, January.
    2. Schönbucher, Philipp J., 2000. "A Libor Market Model with Default Risk," Bonn Econ Discussion Papers 15/2001, University of Bonn, Bonn Graduate School of Economics (BGSE).
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    Citations

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    Cited by:

    1. Barbara Choroś-Tomczyk & Wolfgang Karl H�rdle & Ludger Overbeck, 2014. "Copula dynamics in CDOs," Quantitative Finance, Taylor & Francis Journals, vol. 14(9), pages 1573-1585, September.
    2. Xixuan Han & Boyu Wei & Hailiang Yang, 2018. "Index Options And Volatility Derivatives In A Gaussian Random Field Risk-Neutral Density Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-41, June.
    3. Tao Peng, 2010. "Portfolio Credit Risk Modelling and CDO Pricing - Analytics and Implied Trees from CDO Tranches," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2010.
    4. El Karoui, Nicole & Jeanblanc, Monique & Jiao, Ying, 2017. "Dynamics of multivariate default system in random environment," Stochastic Processes and their Applications, Elsevier, vol. 127(12), pages 3943-3965.
    5. Nicole El Karoui & Monique Jeanblanc & Ying Jiao, 2017. "Dynamics of multivariate default system in random environment," Post-Print hal-01205753, HAL.
    6. Stefan Tappe, 2022. "Invariant cones for jump-diffusions in infinite dimensions," Papers 2206.13913, arXiv.org, revised Nov 2023.
    7. Biagini, Francesca & Mazzon, Andrea & Oberpriller, Katharina, 2023. "Reduced-form framework for multiple ordered default times under model uncertainty," Stochastic Processes and their Applications, Elsevier, vol. 156(C), pages 1-43.
    8. Zehra Eksi & Damir Filipovi'c, 2020. "Affine Pricing and Hedging of Collateralized Debt Obligations," Papers 2011.10101, arXiv.org.
    9. Jan Kallsen & Paul Krühner, 2015. "On a Heath–Jarrow–Morton approach for stock options," Finance and Stochastics, Springer, vol. 19(3), pages 583-615, July.
    10. Ernst Eberlein & Zorana Grbac & Thorsten Schmidt, 2010. "Discrete tenor models for credit risky portfolios driven by time-inhomogeneous L\'evy processes," Papers 1006.2012, arXiv.org, revised Apr 2013.
    11. Francesca Biagini & Andrea Mazzon & Katharina Oberpriller, 2021. "Reduced-form framework for multiple ordered default times under model uncertainty," Papers 2108.04047, arXiv.org, revised Oct 2022.

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