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Nested Simulation in Portfolio Risk Measurement

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Author Info

  • Michael B. Gordy

    ()
    (Federal Reserve Board, Washington, DC 20551)

  • Sandeep Juneja

    ()
    (School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai 400005, India)

Abstract

Risk measurement for derivative portfolios almost invariably calls for nested simulation. In the outer step, one draws realizations of all risk factors up to the horizon, and in the inner step, one reprices each instrument in the portfolio at the horizon conditional on the drawn risk factors. Practitioners may perceive the computational burden of such nested schemes to be unacceptable and adopt a variety of second-best pricing techniques to avoid the inner simulation. In this paper, we question whether such short cuts are necessary. We show that a relatively small number of trials in the inner step can yield accurate estimates, and we analyze how a fixed computational budget may be allocated to the inner and the outer step to minimize the mean square error of the resultant estimator. Finally, we introduce a jackknife procedure for bias reduction.

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File URL: http://dx.doi.org/10.1287/mnsc.1100.1213
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 56 (2010)
Issue (Month): 10 (October)
Pages: 1833-1848

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Handle: RePEc:inm:ormnsc:v:56:y:2010:i:10:p:1833-1848

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Related research

Keywords: nested simulation; loss distribution; value-at-risk; expected shortfall; jackknife estimator;

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References

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  1. repec:fth:inseep:2000-05 is not listed on IDEAS
  2. C. Gourieroux & J.P. Laurent & O. Scaillet, 2000. "Sensitivity analysis of values at risk," THEMA Working Papers 2000-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  3. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
  4. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
  5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  6. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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Citations

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Cited by:
  1. Gordy, Michael B. & Marrone, James, 2012. "Granularity adjustment for mark-to-market credit risk models," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1896-1910.
  2. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers 2013-27, Centre de Recherche en Economie et Statistique.
  3. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
  4. Matthieu Chauvigny & Laurent Devineau & Stéphane Loisel & Véronique Maume-Deschamps, 2011. "Fast remote but not extreme quantiles with multiple factors. Applications to Solvency II and Enterprise Risk Management," Post-Print hal-00517766, HAL.
  5. Nteukam T., Oberlain & Planchet, Frédéric, 2012. "Stochastic evaluation of life insurance contracts: Model point on asset trajectories and measurement of the error related to aggregation," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 624-631.

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