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Nested simulation in portfolio risk measurement

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  • Michael B. Gordy
  • Sandeep Juneja

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 re-prices 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 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 and a dynamic allocation scheme for improved efficiency.

Suggested Citation

  • Michael B. Gordy & Sandeep Juneja, 2008. "Nested simulation in portfolio risk measurement," Finance and Economics Discussion Series 2008-21, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2008-21
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    References listed on IDEAS

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    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.
    2. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
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    4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    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. Vadim Lesnevski & Barry L. Nelson & Jeremy Staum, 2007. "Simulation of Coherent Risk Measures Based on Generalized Scenarios," Management Science, INFORMS, vol. 53(11), pages 1756-1769, November.
    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: The Journal of the International Actuarial Association, Cambridge University Press, vol. 37(02), 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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    Citations

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    Cited by:

    1. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.
    2. David Barrera & Stéphane Crépey & Babacar Diallo & Gersende Fort & Emmanuel Gobet & Uladzislau Stazhynski, 2018. "Stochastic Approximation Schemes for Economic Capital and Risk Margin Computations," Working Papers hal-01710394, HAL.
    3. Helin Zhu & Tianyi Liu & Enlu Zhou, 2015. "Risk Quantification in Stochastic Simulation under Input Uncertainty," Papers 1507.06015, arXiv.org, revised Dec 2017.
    4. 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.
    5. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org.
    6. Andrzej Ruszczynski & Jianing Yao, 2017. "A Dual Method For Backward Stochastic Differential Equations with Application to Risk Valuation," Papers 1701.06234, arXiv.org.
    7. Fermanian, Jean-David, 2014. "The limits of granularity adjustments," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 9-25.
    8. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers 2013-27, Center for Research in Economics and Statistics.
    9. 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.
    10. Cornelis S. L. de Graaf & Drona Kandhai & Christoph Reisinger, 2016. "Efficient exposure computation by risk factor decomposition," Papers 1608.01197, arXiv.org, revised Feb 2018.
    11. 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.
    12. Kleijnen, Jack P.C., 2017. "Regression and Kriging metamodels with their experimental designs in simulation: A review," European Journal of Operational Research, Elsevier, vol. 256(1), pages 1-16.
    13. repec:spr:finsto:v:22:y:2018:i:1:d:10.1007_s00780-017-0347-1 is not listed on IDEAS
    14. Sascha Desmettre & Ralf Korn & Javier Alejandro Varela & Norbert Wehn, 2016. "Nested MC-Based Risk Measurement of Complex Portfolios: Acceleration and Energy Efficiency," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-35, October.
    15. Ankirchner, Stefan & Schneider, Judith C. & Schweizer, Nikolaus, 2014. "Cross-hedging minimum return guarantees: Basis and liquidity risks," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 93-109.
    16. repec:bpj:mcmeap:v:23:y:2017:i:1:p:21-42:n:3 is not listed on IDEAS

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    Keywords

    Financial risk management ; Econometric models ; Jackknife (Statistics);

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