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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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9177.

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Date of creation: Sep 2002
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Publication status: published as Dembo, Amir, Jean-Dominique Deuschel and Darrell Duffie. "Large Portfolio Losses," Finance and Stochastics, 2004, v8(1), 3-16.
Handle: RePEc:nbr:nberwo:9177

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Cited by:
  1. Govindaraj, Suresh, 2005. "Hypothesis testing for diffusion processes with continuous observations: Direct computation of large deviation results for error probabilities," Finance Research Letters, Elsevier, Elsevier, vol. 2(4), pages 234-247, December.
  2. 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, Elsevier, vol. 121(12), pages 2861-2898.
  3. 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.
  4. Eisenberg, Larry, 2011. "Destabilizing properties of a VaR or probability-of-ruin constraint when variances may be infinite," Journal of Financial Stability, Elsevier, Elsevier, vol. 7(1), pages 10-18, January.
  5. Horst, Ulrich, 2007. "Stochastic cascades, credit contagion, and large portfolio losses," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 63(1), pages 25-54, May.
  6. Paolo Dai Pra & Marco Tolotti, 2008. "Heterogeneous credit portfolios and the dynamics of the aggregate losses," Papers 0806.3399, arXiv.org.
  7. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 33(1), pages 15-36, January.
  8. Konstantinos Spiliopoulos, 2014. "Systemic Risk and Default Clustering for Large Financial Systems," Papers 1402.5352, arXiv.org.
  9. Konstantinos Spiliopoulos & Richard B. Sowers, 2013. "Default Clustering in Large Pools: Large Deviations," Papers 1311.0498, arXiv.org.
  10. 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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