基于多小波降噪—分形标幅双集成法的股指期货套期保值比率估计研究

doi:10.16381/j.cnki.issn1003-207x.2024.1454

中国管理科学 ›› 2026, Vol. 34 ›› Issue (5): 21-34.doi: 10.16381/j.cnki.issn1003-207x.2024.1454cstr: 32146.14.j.cnki.issn1003-207x.2024.1454

基于多小波降噪—分形标幅双集成法的股指期货套期保值比率估计研究

朱鹏飞¹^,², 卢团团³(), 魏宇⁴, 林莎⁵

^1.浙江工业大学经济学院，浙江杭州 310014
^2.浙江工业大学现代化产业体系研究院，浙江杭州 310014
^3.浙江财经大学管理学院，浙江杭州 310018
^4.云南财经大学金融学院，云南昆明 650221
^5.浙江工商大学金融学院，浙江杭州 310018

收稿日期:2024-08-26 修回日期:2025-01-14 出版日期:2026-05-25 发布日期:2026-04-21
通讯作者: 卢团团 E-mail:lutuantuan0624@163.com
基金资助:
国家自然科学基金项目(72401260);国家自然科学基金项目(72304241);浙江省自然科学基金项目(LQ23G010007);浙江省自然科学基金项目(LQ23G030003);浙江省哲学社会科学规划年度常规课题(26NDJC020YB);浙江工业大学人文社会科学研究基金年度项目(SKY-ZX-20240015);浙江省属高校基本科研业务费专项资金项目(GB202503002);浙江财经大学新经济统计监测与智能决策研究战略性学科团队资助

Research on Estimating Hedging Ratio in Stock Futures Using a Multi-Wavelet Denoising and Fractal Scale-Amplitude Dual Integration Method

Pengfei Zhu¹^,², Tuantuan Lu³(), Yu Wei⁴, Sha Lin⁵

^1.School of Economics，Zhejiang University of Technology，Hangzhou，Zhejiang 310014，China
^2.Institute for Industrial System Modernization，Zhejiang University of Technology，Hangzhou，Zhejiang 310014，China
^3.School of Management，Zhejiang University of Finance & Economics，Hangzhou，Zhejiang 310018，China
^4.School of Finance，Yunnan University of Finance and Economics，Kunming，Yunnan 650221，China
^5.School of Finance，Zhejiang Gongshang University，Hangzhou，Zhejiang 310018，China

Received:2024-08-26 Revised:2025-01-14 Online:2026-05-25 Published:2026-04-21
Contact: Tuantuan Lu E-mail:lutuantuan0624@163.com

摘要/Abstract

摘要：

本文提出多小波降噪-分形标幅双集成法，以有效应对期现货噪声问题，并充分利用多时间标度和多波动幅度双重价值，从而估计中国股指期货最优套期保值比率。该方法在综合利用多小波函数降低数据噪声基础上，厘定期现货多重分形特征，以计算多波动幅度下多时间标度上套保比率，进而基于群智能优化算法估计标幅双重集成套期保值比率，尽可能提高风险管理效果。以沪深300期现货为例，实证结果表明，该全新模型在绝大部分情况下优于对照组，在大部分指标上具有优势，获得最佳套期保值效果。本文在理论上为套期保值比率研究提供新技术，在实践上为风险管理方案提供新思路。

关键词: 套期保值比率, 中国股指期货, 小波方法, 多重分形模型, 多小波降噪-分形标幅双集成法

Abstract:

The high volatility of Chinese stock market presents significant challenges to its sustainable development. Futures-spot hedging strategies are widely recognized as an effective solution for mitigating stock price risks. Therefore， it seeks to develop a novel and effective model for estimating futures-spot hedge ratios， thereby enabling investors to reduce risks and enhance returns. Considering the presence of substantial noise and multifractal characteristics in futures and spot markets， a multi-wavelet denoising and fractal scale-amplitude dual integration method is introduced for estimating stock futures hedge ratios. This method addresses market noise while fully leveraging the values of multiple time scales and fluctuation amplitudes. It begins by reducing data noise by a multi-wavelet approach and then employs the MF-DCCA （Multifractal Detrended Cross-Correlation Analysis） method to capture multifractal characteristics in futures-spot dependence structure. This process calculates hedging ratios across both volatility amplitudes and time scales. Using a swarm intelligence optimization algorithm， with return maximization and variance minimization as multi-objective functions， this method further integrates the hedging ratios across multiple scales and multiple fluctuation amplitudes sequentially to obtain the dual-integrated hedging ratio. Drawing on the prices from January 3， 2017， to June 14， 2024， totaling 1，808 trading days， this novel method is applied to estimate hedge ratios for the CSI 300 futures and spot markets. Empirical results indicate that， compared to single-wavelet methods， the proposed multi-wavelet denoising approach is more effective at reducing noise and demonstrates superior stability. The findings underscore the critical importance of addressing noise in hedging modeling process. Moreover， the CSI 300 futures and spot markets exhibit significantly multifractal characteristics， with notable variations across different time scales and fluctuation amplitudes. Additionally， the proposed model surpasses control methods in most cases， achieving higher returns， variance reduction ratios， and return-to-variance ratios， thereby delivering the optimal hedging effectiveness. The current paper provides a novel hedging theoretical methodology and offers a new risk-management insight.

Key words: hedging ratio, chinese stock futures, wavelet approach, multifractal model, multi-wavelet denoising and fractal scale-amplitude dual integration method

中图分类号:

F830.9

朱鹏飞,卢团团,魏宇, 等. 基于多小波降噪—分形标幅双集成法的股指期货套期保值比率估计研究[J]. 中国管理科学, 2026, 34(5): 21-34.

Pengfei Zhu,Tuantuan Lu,Yu Wei, et al. Research on Estimating Hedging Ratio in Stock Futures Using a Multi-Wavelet Denoising and Fractal Scale-Amplitude Dual Integration Method[J]. Chinese Journal of Management Science, 2026, 34(5): 21-34.

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类别	均值	标准差	偏度	峰度	JB	Q(5)	Q(10)	ADF
期货	9.26E-5	0.005	-1.299	35.441	67787.15^***	2193.90^***	2305.90^***	-12.816^***
现货	8.89E-5	0.004	-0.709	14.899	9189.98^***	3085.10^***	3238.20^***	-12.846^***

指标	1	2	3	4	5	6	7	8	9	10
AAR	4.13E-4	3.99E-4	4.01E-4	3.86E-4	3.99E-4	4.17E-4	3.38E-4	5.11E-4	4.05E-4	5.15E-4#
VRR	0.920	0.945	0.946	0.938	0.945	0.953	0.896	0.948	0.954	0.956#
RVR	0.166	0.192	0.196	0.175	0.192	0.218	0.119	0.253	0.213	0.277#

指标	1	2	3	4	5	6	7	8	9	10
AAR	1.08E-4	7.30E-5	4.69E-5	7.33E-5	7.31E-5	6.97E-5	1.15E-4	3.24E-5	-7.88E-5	1.23E-4#
VRR	0.941	0.949	0.949	0.945	0.949	0.953#	0.916	0.943	0.917	0.948
RVR	0.049	0.035	0.023	0.034	0.035	0.035	0.043	0.015	NA	0.059#

指标	1	2	3	4	5	6	7	8	9	10
AAR	2.84E-4	2.52E-4	2.53E-4	2.43E-4	2.52E-4	2.63E-4	2.14E-4	3.22E-4#	2.94E-4	2.71E-4
VRR	0.924	0.942	0.943	0.935	0.942	0.950	0.893	0.937	0.947	0.958#
RVR	0.118	0.120	0.122	0.109	0.120	0.135	0.075	0.147	0.147	0.152#

指标	1	2	3	4	5	6	7	8	9	10
AAR	3.49E-4	2.98E-4	3.01E-4	2.93E-4	3.00E-4	3.12E-4	2.55E-4	4.08E-4	3.51E-4	4.31E-4#
VRR	0.914	0.935	0.937	0.932	0.937	0.942	0.890	0.920	0.944#	0.942
RVR	0.138	0.136	0.139	0.130	0.138	0.150	0.089	0.167	0.171	0.206#

基于多小波降噪—分形标幅双集成法的股指期货套期保值比率估计研究

Research on Estimating Hedging Ratio in Stock Futures Using a Multi-Wavelet Denoising and Fractal Scale-Amplitude Dual Integration Method

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参考文献 38

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指标	多小波降噪-分形标幅双集成法-FPA	多小波降噪-分形标幅双集成法-MOFA
AAR	5.24E-4#	5.15E-4
VRR	0.953	0.956#
RVR	0.273	0.277#

保证金	1	2	3	4	5	6	7	8	9	10
保证金8%	4.10E-4	3.96E-4	3.99E-4	3.84E-4	3.97E-4	4.14E-4	3.36E-4	5.07E-4	3.99E-4	5.12E-4#
保证金10%	4.10E-4	3.96E-4	3.98E-4	3.83E-4	3.96E-4	4.14E-4	3.36E-4	5.06E-4	3.99E-4	5.11E-4#
保证金20%	4.07E-4	3.93E-4	3.95E-4	3.80E-4	3.93E-4	4.11E-4	3.34E-4	5.02E-4	3.97E-4	5.08E-4#

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