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Large Portfolio Losses

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  • Amir Dembo
  • Jean-Deominique Deuschel
  • Darrell Duffie

Abstract

This paper provide a large-deviations approximation of the tail distribution of total financial losses on a portfolio consisting of many positions. Applications include the total default losses on a bank portfolio, or the total claims against an insurer. The results may be useful in allocating exposure limits, and in allocating risk capital across different lines of business. Assuming that, for a given total loss, the distress caused by the loss is larger if the loss occurs within a smaller time period, we provide a large-deviations estimate of the likelihood that there will exist a sub-period of the future planning period during which a total loss of the critical severity occurs. Under conditions, this calculation is reduced to the calculation of the likelihood of the same sized loss over a fixed initial time interval whose length is a property of the portfolio and the critical loss level.

Suggested Citation

  • Amir Dembo & Jean-Deominique Deuschel & Darrell Duffie, 2002. "Large Portfolio Losses," NBER Working Papers 9177, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:9177 Note: AP
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    5. Michael D. Bordo & Antu P. Murshid, 2000. "Are Financial Crises Becoming Increasingly More Contagious? What is the Historical Evidence on Contagion?," NBER Working Papers 7900, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Andrew W Lo, 2016. "Moore's Law vs. Murphy's Law in the financial system: who's winning?," BIS Working Papers 564, Bank for International Settlements.
    2. Mengzhe Zhang & Leunglung Chan, 2016. "Saddlepoint approximations to option price in a regime-switching model," Annals of Finance, Springer, vol. 12(1), pages 55-69, February.
    3. Horst, Ulrich, 2007. "Stochastic cascades, credit contagion, and large portfolio losses," Journal of Economic Behavior & Organization, Elsevier, vol. 63(1), pages 25-54, May.
    4. Sergey Nadtochiy & Mykhaylo Shkolnikov, 2017. "Particle systems with singular interaction through hitting times: application in systemic risk modeling," Papers 1705.00691, arXiv.org.
    5. Konstantinos Spiliopoulos & Richard B. Sowers, 2013. "Default Clustering in Large Pools: Large Deviations," Papers 1311.0498, arXiv.org, revised Feb 2015.
    6. Govindaraj, Suresh, 2005. "Hypothesis testing for diffusion processes with continuous observations: Direct computation of large deviation results for error probabilities," Finance Research Letters, Elsevier, vol. 2(4), pages 234-247, December.
    7. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org, revised Feb 2015.
    8. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
    9. Uberti, Pierpaolo & Figini, Silvia, 2010. "How to measure single-name credit risk concentrations," European Journal of Operational Research, Elsevier, vol. 202(1), pages 232-238, April.
    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. Eisenberg, Larry, 2011. "Destabilizing properties of a VaR or probability-of-ruin constraint when variances may be infinite," Journal of Financial Stability, Elsevier, vol. 7(1), pages 10-18, January.
    12. Spiliopoulos, Konstantinos & Sowers, Richard B., 2011. "Recovery rates in investment-grade pools of credit assets: A large deviations analysis," Stochastic Processes and their Applications, Elsevier, vol. 121(12), pages 2861-2898.
    13. Richard B. Sowers, 2009. "Exact Pricing Asymptotics of Investment-Grade Tranches of Synthetic CDO's Part I: A Large Homogeneous Pool," Papers 0903.4475, arXiv.org.
    14. Huyen Pham, 2007. "Some applications and methods of large deviations in finance and insurance," Papers math/0702473, arXiv.org, revised Feb 2007.

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