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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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 10 (2007)
Issue (Month): 04 ()
Pages: 607-631

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Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:04:p:607-631

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Related research

Keywords: Loss distribution; single name default dynamics; cluster default dynamics; calibration; generalized Poisson processes; stochastic intensity; spread dynamics; common Poisson shock models;

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Cited by:
  1. Damiano Brigo & Andrea Pallavicini & Roberto Torresetti, 2009. "Credit models and the crisis, or: how I learned to stop worrying and love the CDOs," Science & Finance (CFM) working paper archive 0912.5427, Science & Finance, Capital Fund Management, revised Feb 2010.
  2. Torresetti, Roberto & Pallavicini, Andrea, 2007. "Stressing rating criteria allowing for default clustering: the CPDO case," MPRA Paper 17104, University Library of Munich, Germany, revised 04 Sep 2009.
  3. 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.
  4. 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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