Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement

• 成果类型: Article
• 署名作者: Hong, L. Jeff; Juneja, Sandeep; Liu, Guangwu
• 署名单位: City University of Hong Kong; City University of Hong Kong; Tata Institute of Fundamental Research (TIFR)
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1591
• 发表日期: 2017
• 页码: 657-673
• 关键词: EXPECTED SHORTFALL; Nonparametric Regression; simulation; options

摘要

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.