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Cluster-Based Extension Of The Generalized Poisson Loss Dynamics And Consistency With Single Names

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  • DAMIANO BRIGO

    (Credit Models Banca IMI, Corso Matteotti 6, 20121 Milano, Italy)

  • ANDREA PALLAVICINI

    (Credit Models Banca IMI, Corso Matteotti 6, 20121 Milano, Italy)

  • ROBERTO TORRESETTI

    (Credit Models Banca IMI, Corso Matteotti 6, 20121 Milano, Italy)

Abstract

We extend the common Poisson shock framework reviewed for example in Lindskog and McNeil [15] to a formulation avoiding repeated defaults, thus obtaining a model that can account consistently for single name default dynamics, cluster default dynamics and default counting process. This approach allows one to introduce significant dynamics, improving on the standard "bottom-up" approaches, and to achieve true consistency with single names, improving on most "top-down" loss models. Furthermore, the resulting GPCL model has important links with the previous GPL dynamical loss model in Brigo et al. [6], which we point out. Model extensions allowing for more articulated spread and recovery dynamics are hinted at. Calibration to both DJi-TRAXX and CDX index and tranche data across attachments and maturities shows that the GPCL model has the same calibration power as the GPL model while allowing for consistency with single names.

Suggested Citation

  • Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2007. "Cluster-Based Extension Of The Generalized Poisson Loss Dynamics And Consistency With Single Names," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 607-631.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:04:n:s0219024907004342
    DOI: 10.1142/S0219024907004342
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    Cited by:

    1. Tomasz R. Bielecki & Areski Cousin & Stéphane Crépey & Alexander Herbertsson, 2014. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model," Journal of Optimization Theory and Applications, Springer, vol. 161(1), pages 90-102, April.
    2. Bielecki, T.R. & Cousin, A. & Crépey, S. & Herbertsson, Alexander, 2012. "A Markov Copula Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries," Working Papers in Economics 545, University of Gothenburg, Department of Economics.
    3. Stéphane Crépey & Shiqi Song, 2014. "Counterparty risk and funding: Immersion and beyond," Working Papers hal-00989062, HAL.
    4. Brigo, Damiano & Mai, Jan-Frederik & Scherer, Matthias, 2016. "Markov multi-variate survival indicators for default simulation as a new characterization of the Marshall–Olkin law," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 60-66.
    5. Bielecki, Tomasz R. & Cousin, Areski & Crépey, Stéphane & Herbertsson, Alexander, 2011. "Dynamic Hedging of Portfolio Credit Risk in a Markov Copula Model (Previous title: Dynamic Modeling of Portfolio Credit Risk with Common Shocks)," Working Papers in Economics 502, University of Gothenburg, Department of Economics, revised 12 Oct 2012.

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