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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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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    3. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    4. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    5. 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.
    6. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    7. Mark Britten-Jones & Stephen M. Schaefer, 1999. "Non-Linear Value-at-Risk," Review of Finance, European Finance Association, vol. 2(2), pages 161-187.
    8. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    9. 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.
    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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