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Heterogeneous credit portfolios and the dynamics of the aggregate losses

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  • Paolo Dai Pra
  • Marco Tolotti

Abstract

We study the impact of contagion in a network of firms facing credit risk. We describe an intensity based model where the homogeneity assumption is broken by introducing a random environment that makes it possible to take into account the idiosyncratic characteristics of the firms. We shall see that our model goes behind the identification of groups of firms that can be considered basically exchangeable. Despite this heterogeneity assumption our model has the advantage of being totally tractable. The aim is to quantify the losses that a bank may suffer in a large credit portfolio. Relying on a large deviation principle on the trajectory space of the process, we state a suitable law of large number and a central limit theorem useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.

Suggested Citation

  • Paolo Dai Pra & Marco Tolotti, 2008. "Heterogeneous credit portfolios and the dynamics of the aggregate losses," Papers 0806.3399, arXiv.org.
  • Handle: RePEc:arx:papers:0806.3399
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    References listed on IDEAS

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    1. Huyen Pham, 2007. "Some applications and methods of large deviations in finance and insurance," Papers math/0702473, arXiv.org, revised Feb 2007.
    2. Paolo Dai Pra & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
    3. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
    4. Crouhy, Michel & Galai, Dan & Mark, Robert, 2000. "A comparative analysis of current credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 59-117, January.
    5. Amir Dembo & Jean-Dominique Deuschel & Darrell Duffie, 2004. "Large portfolio losses," Finance and Stochastics, Springer, vol. 8(1), pages 3-16, January.
    6. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
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    Cited by:

    1. Colapinto, Cinzia & Sartori, Elena & Tolotti, Marco, 2014. "Awareness, persuasion, and adoption: Enriching the Bass model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 1-10.
    2. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
    3. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    4. Cinzia Colapinto & Elena Sartori & Marco Tolotti, 2012. "A two-stage model for diffusion of innovations," Working Papers 16, Department of Management, Università Ca' Foscari Venezia.
    5. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers & Justin A. Sirignano, 2011. "Large Portfolio Asymptotics for Loss From Default," Papers 1109.1272, arXiv.org, revised Feb 2015.
    6. Konstantinos Spiliopoulos & Richard B. Sowers, 2013. "Default Clustering in Large Pools: Large Deviations," Papers 1311.0498, arXiv.org, revised Feb 2015.
    7. Konstantinos Spiliopoulos & Justin A. Sirignano & Kay Giesecke, 2013. "Fluctuation Analysis for the Loss From Default," Papers 1304.1420, arXiv.org, revised Feb 2015.

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