基于近邻截断的跳跃扩散过程波动函数的设定检验

doi:10.16381/j.cnki.issn1003-207x.2020.07.005

中国管理科学 ›› 2020, Vol. 28 ›› Issue (7): 45-56.doi: 10.16381/j.cnki.issn1003-207x.2020.07.005

基于近邻截断的跳跃扩散过程波动函数的设定检验

陈强^1,2, 龚玉婷³

1. 上海财经大学经济学院, 上海 200433;
2. 上海财经大学数理经济学重点实验室, 上海 200433;
3. 上海大学悉尼工商学院, 上海 201800

收稿日期:2017-06-27 修回日期:2017-11-30 出版日期:2020-07-20 发布日期:2020-08-04
通讯作者: 陈强(1982-),男(汉族),福建寿宁人,上海财经大学经济学院,副教授,博导,研究方向:金融计量与金融市场,E-mail:chen.qiang@mail.shufe.edu.cn. E-mail:chen.qiang@mail.shufe.edu.cn
基金资助:
国家自然科学基金资助项目（71501120，71601108，71701118）；教育部人文社会科学基金资助项目（20YJC790013）

Specification Test of Volatility Functions in Jump Diffusion Processes using Nearest Neighbor Truncation

CHEN Qiang^1,2, GONG Yu-ting³

1. School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China;
2. Key Laboratory of Mathematical Economics(SUFE), Ministry of Education, Shanghai 200433, China;
3. SHU-UTS SILC Business School, Shanghai University, Shanghai 201800, China

Received:2017-06-27 Revised:2017-11-30 Online:2020-07-20 Published:2020-08-04

摘要/Abstract

摘要： 高频数据环境下的波动函数设定检验容易受到数据中跳跃的影响。为此，本文基于近邻截断（nearest neighbor truncation）方法，利用残差构造部分和（partial sum）过程构造出波动函数参数形式的设定检验方法，并分析了该检验方法在原假设条件下的近似极限性质与自助检验步骤。所提出的波动函数设定检验方法能渐近有效的避免跳跃扩散过程的漂移项与跳跃项的影响。蒙特卡洛模拟结果表明这些检验方法对跳跃的影响具有稳健性，且具有合理的检验水平（size）和检验功效（power）。利用这些检验方法对我国的上海银行间同业拆放利率（Shibor）数据进行实证分析，结果表明本文所提出的跳跃稳健的波动函数检验方法比非跳跃稳健的波动函数检验方法具有更好的区分度。

关键词: 波动函数, 跳跃扩散过程, 设定检验, 部分和过程, 近邻截断

Abstract: Since the volatility function testing is sensitive to jumps in high frequency data, based on nearest neighbor truncation approach,new tests for volatility function form of jump diffusion models are constructed by thepartial sum residual processes. The tests approximating asymptotic properties and their bootstrap methods are investigated. The test statistics are asymptotically robust to the drift and jump terms in jump diffusions. Monte Carlo simulations show that the tests are robust to jumps, and have reasonable size and power performances. The proposed tests are applied to the data of Shanghai Interbank Offered Rate (Shibor), it is found that the jump robust tests can distinguish models better than non-robust tests.

Key words: volatility function, jump diffusion processes, specification test, partial sum processes, nearest neighbor truncation

中图分类号:

O212

陈强, 龚玉婷. 基于近邻截断的跳跃扩散过程波动函数的设定检验[J]. 中国管理科学, 2020, 28(7): 45-56.

CHEN Qiang, GONG Yu-ting. Specification Test of Volatility Functions in Jump Diffusion Processes using Nearest Neighbor Truncation[J]. Chinese Journal of Management Science, 2020, 28(7): 45-56.

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基于近邻截断的跳跃扩散过程波动函数的设定检验

Specification Test of Volatility Functions in Jump Diffusion Processes using Nearest Neighbor Truncation

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