Kernel smoothing for nested estimation with application to portfolio risk measurement

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)657-673
Journal / PublicationOperations Research
Issue number3
Online published12 Apr 2017
Publication statusPublished - May 2017


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.

Research Area(s)

  • Kernel estimation, Nested estimation, Portfolio risk measurement