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Large portfolio losses: A dynamic contagion model

Author

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  • Paolo Dai Pra
  • Wolfgang J. Runggaldier
  • Elena Sartori
  • Marco Tolotti

Abstract

Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the "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 & Wolfgang J. Runggaldier & Elena Sartori & Marco Tolotti, 2007. "Large portfolio losses: A dynamic contagion model," Papers 0704.1348, arXiv.org, revised Mar 2009.
  • Handle: RePEc:arx:papers:0704.1348
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    File URL: http://arxiv.org/pdf/0704.1348
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    References listed on IDEAS

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    1. Umut Çetin & Robert Jarrow & Philip Protter & Yildiray Yildirim, 2008. "Modeling Credit Risk With Partial Information," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 23, pages 579-590 World Scientific Publishing Co. Pte. Ltd..
    2. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    3. 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..
    4. Horst, Ulrich, 2007. "Stochastic cascades, credit contagion, and large portfolio losses," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 25-54, May.
    5. 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.
    6. 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.
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    Citations

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    Cited by:

    1. Emilio Barucci & Marco Tolotti, 2012. "Identity, reputation and social interaction with an application to sequential voting," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 7(1), pages 79-98, May.
    2. Paolo Dai Pra & Fulvio Fontini & Elena Sartori & Marco Tolotti, 2011. "Endogenous equilibria in liquid markets with frictions and boundedly rational agents," Working Papers 7, Department of Management, Università Ca' Foscari Venezia.
    3. Agostino Capponi & Martin Larsson, 2011. "Default and Systemic Risk in Equilibrium," Papers 1108.1133, arXiv.org, revised Dec 2011.
    4. Igor Prünster & Matteo Ruggiero, 2011. "A Bayesian nonparametric approach to modeling market share dynamics," Carlo Alberto Notebooks 217, Collegio Carlo Alberto.
    5. Lijun Bo & Agostino Capponi, 2014. "Bilateral credit valuation adjustment for large credit derivatives portfolios," Finance and Stochastics, Springer, vol. 18(2), pages 431-482, April.
    6. Kay Giesecke & Konstantinos Spiliopoulos & Richard B. Sowers, 2011. "Default clustering in large portfolios: Typical events," Papers 1104.1773, arXiv.org, revised Feb 2013.
    7. Barucci, Emilio & Tolotti, Marco, 2012. "Social interaction and conformism in a random utility model," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1855-1866.
    8. Josselin Garnier & George Papanicolaou & Tzu-Wei Yang, 2015. "A risk analysis for a system stabilized by a central agent," Papers 1507.08333, arXiv.org, revised Aug 2015.
    9. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    10. Dai Pra, Paolo & Tolotti, Marco, 2009. "Heterogeneous credit portfolios and the dynamics of the aggregate losses," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2913-2944, September.
    11. 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.
    12. Konstantinos Spiliopoulos & Richard B. Sowers, 2013. "Default Clustering in Large Pools: Large Deviations," Papers 1311.0498, arXiv.org, revised Feb 2015.
    13. Emilio Barucci & Marco Tolotti, 2009. "The dynamics of social interaction with agents’ heterogeneity," Working Papers 189, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    14. Sergey Nadtochiy & Mykhaylo Shkolnikov, 2017. "Particle systems with singular interaction through hitting times: application in systemic risk modeling," Papers 1705.00691, arXiv.org.
    15. 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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