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A Confidence Interval Procedure for Expected Shortfall Risk Measurement via Two-Level Simulation

Author

Listed:
  • Hai Lan

    (Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China)

  • Barry L. Nelson

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

  • Jeremy Staum

    (Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois 60208)

Abstract

We develop and evaluate a two-level simulation procedure that produces a confidence interval for expected shortfall. The outer level of simulation generates financial scenarios, whereas the inner level estimates expected loss conditional on each scenario. Our procedure uses the statistical theory of empirical likelihood to construct a confidence interval. It also uses tools from the ranking-and-selection literature to make the simulation efficient.

Suggested Citation

  • Hai Lan & Barry L. Nelson & Jeremy Staum, 2010. "A Confidence Interval Procedure for Expected Shortfall Risk Measurement via Two-Level Simulation," Operations Research, INFORMS, vol. 58(5), pages 1481-1490, October.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:5:p:1481-1490
    DOI: 10.1287/opre.1090.0792
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    References listed on IDEAS

    as
    1. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    2. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, August.
    3. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(1), pages 87-107, Winter.
    4. Justin Boesel & Barry L. Nelson & Seong-Hee Kim, 2003. "Using Ranking and Selection to “Clean Up” after Simulation Optimization," Operations Research, INFORMS, vol. 51(5), pages 814-825, October.
    5. 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.
    6. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, August.
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    Citations

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    Cited by:

    1. An Chen & Mitja Stadje & Fangyuan Zhang, 2020. "On the equivalence between Value-at-Risk- and Expected Shortfall-based risk measures in non-concave optimization," Papers 2002.02229, arXiv.org, revised Jun 2022.
    2. Kun Zhang & Guangwu Liu & Shiyu Wang, 2022. "Technical Note—Bootstrap-based Budget Allocation for Nested Simulation," Operations Research, INFORMS, vol. 70(2), pages 1128-1142, March.
    3. Guay, François & Schwenkler, Gustavo, 2021. "Efficient estimation and filtering for multivariate jump–diffusions," Journal of Econometrics, Elsevier, vol. 223(1), pages 251-275.
    4. Kun Zhang & Ben Mingbin Feng & Guangwu Liu & Shiyu Wang, 2022. "Sample Recycling for Nested Simulation with Application in Portfolio Risk Measurement," Papers 2203.15929, arXiv.org.
    5. Qidong Lai & Guangwu Liu & Bingfeng Zhang & Kun Zhang, 2025. "Simulating Confidence Intervals for Conditional Value-at-Risk via Least-Squares Metamodels," INFORMS Journal on Computing, INFORMS, vol. 37(4), pages 1087-1105, July.
    6. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    7. Wenjia Wang & Yanyuan Wang & Xiaowei Zhang, 2024. "Smooth Nested Simulation: Bridging Cubic and Square Root Convergence Rates in High Dimensions," Management Science, INFORMS, vol. 70(12), pages 9031-9057, December.
    8. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    9. L. Jeff Hong & Guangxin Jiang & Ying Zhong, 2022. "Solving Large-Scale Fixed-Budget Ranking and Selection Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2930-2949, November.
    10. Dang, Ou & Feng, Mingbin & Hardy, Mary R., 2023. "Two-stage nested simulation of tail risk measurement: A likelihood ratio approach," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 1-24.
    11. L. Jeff Hong & Sandeep Juneja & Guangwu Liu, 2017. "Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement," Operations Research, INFORMS, vol. 65(3), pages 657-673, June.
    12. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
    13. Runhuan Feng & Peng Li, 2021. "Sample Recycling Method -- A New Approach to Efficient Nested Monte Carlo Simulations," Papers 2106.06028, arXiv.org.
    14. Guo Liang & Kun Zhang & Jun Luo, 2024. "A FAST Method for Nested Estimation," INFORMS Journal on Computing, INFORMS, vol. 36(6), pages 1481-1500, December.
    15. Feng, Ben Mingbin & Li, Johnny Siu-Hang & Zhou, Kenneth Q., 2022. "Green nested simulation via likelihood ratio: Applications to longevity risk management," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 285-301.
    16. Wang, Tianxiang & Xu, Jie & Hu, Jian-Qiang & Chen, Chun-Hung, 2023. "Efficient estimation of a risk measure requiring two-stage simulation optimization," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1355-1365.
    17. Kleijnen, Jack P.C., 2013. "Simulation-Optimization via Kriging and Bootstrapping : A Survey (Revision of CentER DP 2011-064)," Discussion Paper 2013-064, Tilburg University, Center for Economic Research.
    18. Basu, Sanjay, 2011. "Comparing simulation models for market risk stress testing," European Journal of Operational Research, Elsevier, vol. 213(1), pages 329-339, August.
    19. Helin Zhu & Tianyi Liu & Enlu Zhou, 2015. "Risk Quantification in Stochastic Simulation under Input Uncertainty," Papers 1507.06015, arXiv.org, revised Dec 2017.

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