基于门限双幂变差的资产价格时点波动非参数估计

doi:10.16381/j.cnki.issn1003-207x.2016.01.003

中国管理科学 ›› 2016, Vol. 24 ›› Issue (1): 21-29.doi: 10.16381/j.cnki.issn1003-207x.2016.01.003

基于门限双幂变差的资产价格时点波动非参数估计

沈根祥^1,2

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教育部重点实验室, 上海 200433

收稿日期:2014-03-17 修回日期:2015-02-14 出版日期:2016-01-20 发布日期:2016-01-28
通讯作者: 沈根祥(1964-),男(汉族),河南许昌人,上海财经大学教授,博士生导师,研究方向:金融计量学,金融市场数量分析,E-mail:syxman@shufe.edu.cn. E-mail:syxman@shufe.edu.cn
基金资助:
教育部人文社科研究规划基金资助项目(13YJA790095)资助;上海财经大学数量经济教育部重点实验室开放课题资助(201301KF01)

Nonparametric Estimation for Spot Volatility of Asset Price Using Bipower Variations

SHEN Gen-xiang^1,2

1. School of Econmics, Shanghai University of Finance and Economics, Shanghai 200433, China;
2. Key Laboratory of Mathematical Ecnomics(SUFE), Ministry of Education, Shanghai 200433, China

Received:2014-03-17 Revised:2015-02-14 Online:2016-01-20 Published:2016-01-28

摘要/Abstract

摘要： 估计带跳资产价格的时点波动时,需要用门限过滤方法消除跳的影响。在有限样本下,门限过滤会产生错滤偏误和漏虑偏误,降低估计精度。跳错滤产生的偏误可通过对错滤样本进行补足的方法进行纠偏,但由于发生时点未知,跳漏滤产生的偏误无法纠正,只能通过估计量设计来减少漏滤偏误。本文首次提出基于门限双幂变差的时点波动估计量,采用核平滑方法对资产价格时点波动进行非参数估计,有效减少跳错滤导致的偏误。采用随机阵列极限理论,本文证明了估计量的一致性和渐进正态性,在分析有限样本偏误的基础上,给出估计量的纠偏方法。蒙特卡洛模拟表明,本文给出的估计量,漏滤偏误明显小于基于二次变差构造的估计量,对时点波动估计的性质具有实质改进。采用Kupiec动态VaR精度检验对沪深300指数的实证分析表明,本文给出的时点波动估计更能描述资产收益的波动特征。

关键词: 时点波动, Poisson跳, 双幂变差, 核平滑

Abstract: The threshold jump-annihilating method to estimate spot volatility of jump-diffusion asset price processes can miss the small jumps and bring about upward bias. In this paper, a new spot volatility estimator of asset prices is proposed based on bipower variation that reduces significantly finite-sample upward bias from jump-filtering-missing. The consistency and asymptotic normality is established. An extensive Monte Carlo simulation shows that the estimator in the paper outperforms the others in literature. The empirical study using Kupiec test based on sample from CSI300 shows that our spot volatility estimator can capture the feather of market risk more accurately.

Key words: Spot Volatility, Poisson Jumps, Bipower Variation, Kernel Smoothing

中图分类号:

F830.9

沈根祥. 基于门限双幂变差的资产价格时点波动非参数估计[J]. 中国管理科学, 2016, 24(1): 21-29.

SHEN Gen-xiang. Nonparametric Estimation for Spot Volatility of Asset Price Using Bipower Variations[J]. Chinese Journal of Management Science, 2016, 24(1): 21-29.

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基于门限双幂变差的资产价格时点波动非参数估计

Nonparametric Estimation for Spot Volatility of Asset Price Using Bipower Variations

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