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Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement

Author

Listed:
  • L. Jeff Hong

    (Department of Economics and Finance and Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon, Hong Kong)

  • Sandeep Juneja

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

  • Guangwu Liu

    (Department of Management Sciences, College of Business, City University of Hong Kong, Kowloon, Hong Kong)

Abstract

Nested estimation involves estimating an expectation of a function of a conditional expectation via simulation. This problem has of late received increasing attention amongst researchers due to its broad applicability particularly in portfolio risk measurement and in pricing complex derivatives. In this paper, we study a kernel smoothing approach. We analyze its asymptotic properties, and present efficient algorithms for practical implementation. While asymptotic results suggest that the kernel smoothing approach is preferable over nested simulation only for low-dimensional problems, we propose a decomposition technique for portfolio risk measurement, through which a high-dimensional problem may be decomposed into low-dimensional ones that allow an efficient use of the kernel smoothing approach. Numerical studies show that, with the decomposition technique, the kernel smoothing approach works well for a reasonably large portfolio with 200 risk factors. This suggests that the proposed methodology may serve as a viable tool for risk measurement practice.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:65:y:2017:i:3:p:657-673
    DOI: 10.1287/opre.2017.1591
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Nifei Lin & Yingda Song & L. Jeff Hong, 2024. "Efficient Nested Estimation of CoVaR: A Decoupled Approach," Papers 2411.01319, arXiv.org.
    2. 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.
    3. David J. Eckman & Shane G. Henderson & Sara Shashaani, 2023. "Diagnostic Tools for Evaluating and Comparing Simulation-Optimization Algorithms," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 350-367, March.
    4. Runhuan Feng & Peng Li, 2021. "Sample Recycling Method -- A New Approach to Efficient Nested Monte Carlo Simulations," Papers 2106.06028, arXiv.org.
    5. Liu, Xiaoyu & Yan, Xing & Zhang, Kun, 2024. "Kernel quantile estimators for nested simulation with application to portfolio value-at-risk measurement," European Journal of Operational Research, Elsevier, vol. 312(3), pages 1168-1177.
    6. Hongjun Ha & Daniel Bauer, 2022. "A least-squares Monte Carlo approach to the estimation of enterprise risk," Finance and Stochastics, Springer, vol. 26(3), pages 417-459, July.
    7. Youngjun Choe & Henry Lam & Eunshin Byon, 2018. "Uncertainty Quantification of Stochastic Simulation for Black-box Computer Experiments," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1155-1172, December.
    8. Xin Yun & Yanyi Ye & Hao Liu & Yi Li & Kin-Keung Lai, 2023. "Stylized Model of Lévy Process in Risk Estimation," Mathematics, MDPI, vol. 11(6), pages 1-14, March.
    9. Lucio Fernandez‐Arjona & Damir Filipović, 2022. "A machine learning approach to portfolio pricing and risk management for high‐dimensional problems," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 982-1019, October.
    10. Devang Sinha & Siddhartha P. Chakrabarty, 2024. "Multilevel Monte Carlo in Sample Average Approximation: Convergence, Complexity and Application," Papers 2407.18504, arXiv.org.
    11. 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.
    12. Qin, Chang-Xiong & Liu, Zhao, 2022. "Reference price effect of partially similar online products in the consideration stage," Journal of Business Research, Elsevier, vol. 152(C), pages 70-81.
    13. 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.
    14. Qiyun Pan & Eunshin Byon & Young Myoung Ko & Henry Lam, 2020. "Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 524-547, October.
    15. Mingbin Ben Feng & Eunhye Song, 2020. "Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method," Papers 2008.13087, arXiv.org, revised May 2024.
    16. 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.
    17. 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.
    18. Weihuan Huang & Nifei Lin & L. Jeff Hong, 2022. "Monte-Carlo Estimation of CoVaR," Papers 2210.06148, arXiv.org.

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