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Nested Simulation in Portfolio Risk Measurement

Author

Listed:
  • 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.

Suggested Citation

  • Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
  • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:10:p:1833-1848
    DOI: 10.1287/mnsc.1100.1213
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    File URL: http://dx.doi.org/10.1287/mnsc.1100.1213
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    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
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    7. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    8. Kim, Joseph Hyun Tae & Hardy, Mary R., 2007. "Quantifying and Correcting the Bias in Estimated Risk Measures," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 365-386, November.
    9. 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.
    10. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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