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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:

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    3. Weihuan Huang & Nifei Lin & L. Jeff Hong, 2022. "Monte-Carlo Estimation of CoVaR," Papers 2210.06148, arXiv.org.
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    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.
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    11. Mingbin Ben Feng & Eunhye Song, 2020. "Optimal Nested Simulation Experiment Design via Likelihood Ratio Method," Papers 2008.13087, arXiv.org, revised Jul 2021.
    12. 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.
    13. Runhuan Feng & Peng Li, 2021. "Sample Recycling Method -- A New Approach to Efficient Nested Monte Carlo Simulations," Papers 2106.06028, arXiv.org.
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    16. 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.

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