Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement
研究了通过模拟进行嵌套估计的核平滑方法，分析了渐近性质并给出高效算法；针对高维投资组合风险问题提出分解技术，使核平滑在200个风险因子的组合中表现良好。
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. The e-companion is available at https://doi.org/10.1287/opre.2017.1591 .