IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v57y2009i1p118-130.html
   My bibliography  Save this article

Estimating Quantile Sensitivities

Author

Listed:
  • L. Jeff Hong

    (Department of Industrial Engineering and Logistics Management, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China)

Abstract

Quantiles of a random performance serve as important alternatives to the usual expected value. They are used in the financial industry as measures of risk and in the service industry as measures of service quality. To manage the quantile of a performance, we need to know how changes in the input parameters affect the output quantiles, which are called quantile sensitivities. In this paper, we show that the quantile sensitivities can be written in the form of conditional expectations. Based on the conditional-expectation form, we first propose an infinitesimal-perturbation-analysis (IPA) estimator. The IPA estimator is asymptotically unbiased, but it is not consistent. We then obtain a consistent estimator by dividing data into batches and averaging the IPA estimates of all batches. The estimator satisfies a central limit theorem for the i.i.d. data, and the rate of convergence is strictly slower than n -1/3 . The numerical results show that the estimator works well for practical problems.

Suggested Citation

  • L. Jeff Hong, 2009. "Estimating Quantile Sensitivities," Operations Research, INFORMS, vol. 57(1), pages 118-130, February.
    • Handle: RePEc:inm:oropre:v:57:y:2009:i:1:p:118-130
    DOI: 10.1287/opre.1080.0531
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1080.0531
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1080.0531?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Sen, Pranab Kumar, 1972. "On the Bahadur representation of sample quantiles for sequences of [phi]-mixing random variables," Journal of Multivariate Analysis, Elsevier, vol. 2(1), pages 77-95, March.
    2. Xing Jin & Michael C. Fu & Xiaoping Xiong, 2003. "Probabilistic Error Bounds for Simulation Quantile Estimators," Management Science, INFORMS, vol. 49(2), pages 230-246, February.
    3. Rajan Suri & Michael A. Zazanis, 1988. "Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue," Management Science, INFORMS, vol. 34(1), pages 39-64, January.
    4. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    5. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    6. P. Heidelberger & P. A. W. Lewis, 1984. "Quantile Estimation in Dependent Sequences," Operations Research, INFORMS, vol. 32(1), pages 185-209, February.
    7. Athanassios N. Avramidis & James R. Wilson, 1998. "Correlation-Induction Techniques for Estimating Quantiles in Simulation Experiments," Operations Research, INFORMS, vol. 46(4), pages 574-591, August.
    8. Paul Glasserman & Sridhar Tayur, 1995. "Sensitivity Analysis for Base-Stock Levels in Multiechelon Production-Inventory Systems," Management Science, INFORMS, vol. 41(2), pages 263-281, February.
    9. Jason C. Hsu & Barry L. Nelson, 1990. "Control Variates for Quantile Estimation," Management Science, INFORMS, vol. 36(7), pages 835-851, July.
    10. Timothy C. Hesterberg & Barry L. Nelson, 1998. "Control Variates for Probability and Quantile Estimation," Management Science, INFORMS, vol. 44(9), pages 1295-1312, September.
    11. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
    12. Martin I. Reiman & Alan Weiss, 1989. "Sensitivity Analysis for Simulations via Likelihood Ratios," Operations Research, INFORMS, vol. 37(5), pages 830-844, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Samuel N. Cohen & Christoph Reisinger & Sheng Wang, 2022. "Estimating risks of option books using neural-SDE market models," Papers 2202.07148, arXiv.org.
    2. Chen, E. Jack & Kelton, W. David, 2006. "Quantile and tolerance-interval estimation in simulation," European Journal of Operational Research, Elsevier, vol. 168(2), pages 520-540, January.
    3. Hui Dong & Marvin K. Nakayama, 2017. "Quantile Estimation with Latin Hypercube Sampling," Operations Research, INFORMS, vol. 65(6), pages 1678-1695, December.
    4. Huei-Wen Teng, 2023. "Importance Sampling for Calculating the Value-at-Risk and Expected Shortfall of the Quadratic Portfolio with t-Distributed Risk Factors," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1125-1154, October.
    5. Yongqiang Wang & Michael C. Fu & Steven I. Marcus, 2012. "A New Stochastic Derivative Estimator for Discontinuous Payoff Functions with Application to Financial Derivatives," Operations Research, INFORMS, vol. 60(2), pages 447-460, April.
    6. Guangwu Liu & Liu Jeff Hong, 2009. "Kernel estimation of quantile sensitivities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(6), pages 511-525, September.
    7. Michael C. Fu, 2008. "What you should know about simulation and derivatives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(8), pages 723-736, December.
    8. Ye, Wuyi & Zhou, Yi & Chen, Pengzhan & Wu, Bin, 2024. "A simulation-based method for estimating systemic risk measures," European Journal of Operational Research, Elsevier, vol. 313(1), pages 312-324.
    9. Christos Alexopoulos & David Goldsman & Anup C. Mokashi & Kai-Wen Tien & James R. Wilson, 2019. "Sequest: A Sequential Procedure for Estimating Quantiles in Steady-State Simulations," Operations Research, INFORMS, vol. 67(4), pages 1162-1183, July.
    10. Chaitra H. Nagaraja & Haikady N. Nagaraja, 2020. "Distribution‐free Approximate Methods for Constructing Confidence Intervals for Quantiles," International Statistical Review, International Statistical Institute, vol. 88(1), pages 75-100, April.
    11. Wei Jiang & Steven Kou, 2021. "Simulating risk measures via asymptotic expansions for relative errors," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 907-942, July.
    12. Xin Yun & L. Jeff Hong & Guangxin Jiang & Shouyang Wang, 2019. "On gamma estimation via matrix kriging," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 393-410, August.
    13. Xing Jin & Michael C. Fu & Xiaoping Xiong, 2003. "Probabilistic Error Bounds for Simulation Quantile Estimators," Management Science, INFORMS, vol. 49(2), pages 230-246, February.
    14. Xing Jin & Allen X. Zhang, 2006. "Reclaiming Quasi-Monte Carlo Efficiency in Portfolio Value-at-Risk Simulation Through Fourier Transform," Management Science, INFORMS, vol. 52(6), pages 925-938, June.
    15. He, Zhijian, 2022. "Sensitivity estimation of conditional value at risk using randomized quasi-Monte Carlo," European Journal of Operational Research, Elsevier, vol. 298(1), pages 229-242.
    16. Mark J. Cathcart & Steven Morrison & Alexander J. McNeil, 2011. "Calculating Variable Annuity Liability 'Greeks' Using Monte Carlo Simulation," Papers 1110.4516, arXiv.org.
    17. Guangxin Jiang & L. Jeff Hong & Barry L. Nelson, 2020. "Online Risk Monitoring Using Offline Simulation," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 356-375, April.
    18. Mingbin Ben Feng & Eunhye Song, 2020. "Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method," Papers 2008.13087, arXiv.org, revised May 2024.
    19. Shih-Kuei Lin & Ren-Her Wang & Cheng-Der Fuh, 2006. "Risk Management for Linear and Non-Linear Assets: A Bootstrap Method with Importance Resampling to Evaluate Value-at-Risk," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(3), pages 261-295, September.
    20. Peter Christoffersen & Silvia Gonçalves, 2004. "Estimation Risk in Financial Risk Management," CIRANO Working Papers 2004s-15, CIRANO.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:57:y:2009:i:1:p:118-130. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.