基于支持向量机的证券投资风险管理研究
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摘要
风险是影响一切金融活动的基本要素。我国金融市场作为一个发展中的新兴市场,不仅仅是信用风险,市场风险等其他风险也必将随着金融市场的发展而逐渐加大。因此,金融风险管理方法研究对当前及未来我国金融创新以及投资机构进行投资决策均具有重要的意义。/
支持向量机(Support Vector Machine,SVM)是在统计学习理论的基础上发展起来的一种新的机器学习方法,由于其完备的理论基础、出色的学习性能及预测性能而得到了广泛的应用。本文研究基于支持向量机的证券风险管理方法,主要的工作和取得的成果有:
系统总结与回顾了证券市场投资风险度量方法;介绍了基于结构风险最小化原则的支持向量机理论与方法及SVM在经济学中的应用情况并研究了基于SVM的证券价格预测方法。以上海证券交易所综合指数为例的实证研究表明SVM模型能够很好的对股市波动进行建模。以华夏大盘精选基金为例的实证研究表明基于SVM的混沌时间序列预测可以较好捕捉市场运行趋势和识别市场异常波动,是一种优秀的风险预测与管理工具。
针对统计学框架下传统VaR计算方法的不足,发展了基于加权支持向量机(W-SVM)的VaR计算新方法。对2001-2009年上证综指的实证研究表明,基于W-SVM的VaR模型优于传统的VaR方法,在小样本、厚尾、非线性及有异常波动的市场条件下,各种置信度下的W-SVM方法均能取得较好的性能。适合于各种风险偏好投资者采用。
Risk is the basic factor that affects all financial activities. With the development of China's financial markets, not only credit risk, but also market risk and other risks will gradually increase. Thus, financial risk management methods are very important to the present and future innovation and financial institutions investment decisions.
Support Vector Machine (Support Vector Machine, SVM) is based on statistical learning theory, which is a new way for machine learning. Because of its sound theoretical foundation, excellent learning performance and projected performance, SVM has been widely used. In this paper, risk management method based on support vector machine is investigated. The main work and the results achieved are:
Systematically review of stock market investment risk measurement methods; introduced support vector machine theory and methods based on the principle of structural risk minimization; introduced SVM application in the economics. SVM-based prediction method of securities price is studied. Empirical studies for the Shanghai Composite Index have shown that SVM model can model the stock market volatility very well. Empirical studies for the Huaxia foundation have shown that SVM-based prediction of chaotic time series can capture the market trends and identify market fluctuations well and it is an excellent risk prediction and management tools. According to the defects of the traditional VaR computation methods in the statistics framework, a new VaR model based on weighted support vector machine (W-SVM) was investigated. The Shanghai composite index from the year 2001 to 2009 was modeled and the simulation results indicated that the new VAR method based W-SVM is better than traditional methods. Even for small sample, abnormal fluctuations and heavy tails in nonlinear market, W-SVM model can obtain good performance at different confidence intervals. And it is suitable for different investor.
支持向量机(Support Vector Machine,SVM)是在统计学习理论的基础上发展起来的一种新的机器学习方法,由于其完备的理论基础、出色的学习性能及预测性能而得到了广泛的应用。本文研究基于支持向量机的证券风险管理方法,主要的工作和取得的成果有:
系统总结与回顾了证券市场投资风险度量方法;介绍了基于结构风险最小化原则的支持向量机理论与方法及SVM在经济学中的应用情况并研究了基于SVM的证券价格预测方法。以上海证券交易所综合指数为例的实证研究表明SVM模型能够很好的对股市波动进行建模。以华夏大盘精选基金为例的实证研究表明基于SVM的混沌时间序列预测可以较好捕捉市场运行趋势和识别市场异常波动,是一种优秀的风险预测与管理工具。
针对统计学框架下传统VaR计算方法的不足,发展了基于加权支持向量机(W-SVM)的VaR计算新方法。对2001-2009年上证综指的实证研究表明,基于W-SVM的VaR模型优于传统的VaR方法,在小样本、厚尾、非线性及有异常波动的市场条件下,各种置信度下的W-SVM方法均能取得较好的性能。适合于各种风险偏好投资者采用。
Risk is the basic factor that affects all financial activities. With the development of China's financial markets, not only credit risk, but also market risk and other risks will gradually increase. Thus, financial risk management methods are very important to the present and future innovation and financial institutions investment decisions.
Support Vector Machine (Support Vector Machine, SVM) is based on statistical learning theory, which is a new way for machine learning. Because of its sound theoretical foundation, excellent learning performance and projected performance, SVM has been widely used. In this paper, risk management method based on support vector machine is investigated. The main work and the results achieved are:
Systematically review of stock market investment risk measurement methods; introduced support vector machine theory and methods based on the principle of structural risk minimization; introduced SVM application in the economics. SVM-based prediction method of securities price is studied. Empirical studies for the Shanghai Composite Index have shown that SVM model can model the stock market volatility very well. Empirical studies for the Huaxia foundation have shown that SVM-based prediction of chaotic time series can capture the market trends and identify market fluctuations well and it is an excellent risk prediction and management tools. According to the defects of the traditional VaR computation methods in the statistics framework, a new VaR model based on weighted support vector machine (W-SVM) was investigated. The Shanghai composite index from the year 2001 to 2009 was modeled and the simulation results indicated that the new VAR method based W-SVM is better than traditional methods. Even for small sample, abnormal fluctuations and heavy tails in nonlinear market, W-SVM model can obtain good performance at different confidence intervals. And it is suitable for different investor.
引文
[1]王志诚,周春生.金融风险管理研究进展-国际文献综述[J].管理世界,2006(4): 158-169.
[2]严复,海党星,颜文虎.风险管理发展历程和趋势综述[J].管理现代化,2007(2): 30-33.
[3]肖志勇.VaR模型在金融风险管理中的应用[J].生产力研究,2008,2(4):44-46.
[4]秦拯,陈收,邹建军.VaR模型的计算方法及其评析[J].系统工程,2005,23(7):12-16.
[5]王玉玲.CVaR方法在投资组合中的应用[J].统计与决策,2008,2:71-72.
[6]徐元铖.国外风险价值模型研究现状[J].外国经济与管理,2005,27(6):44-51.
[7]周艳菊,邱菀华,王宗润.基于CVaR约束的多产品订货风险决策模型[J].中国管理科学,2006,14(5):62-67.
[8]孟志青,虞晓芬,蒋敏等.基于动态CVaR模型的房地产组合投资的风险度量与控制策略[J].系统工程理论与实践,2007,9:69-76.
[9]刘俊山.基于风险测度理论的VaR与CVaR的比较研究[J].数量经济技术经济研究,2007,3:125-133.
[10]蒋敏,胡奇英,孟志青.基于权值的多阶段风险值证券组合问题研究[J].管理工程学报,2006,20(3):38-40.
[11]刘小茂,杜红军.金融资产的VaR和CVaR风险的优良估计[J].中国管理科学,2006,14(5):1-6.
[12]杨磊,王明征,李文立.两种带有能力(Capacity)约束的报童风险模型最优策略[J].系统工程理论与实践,2008,5:35-42.
[13]韩国文.股票流动性风险测度模型的构建与实证分析[J].中国管理科学,2008,16(2):1-6.
[14]张鹏.不允许卖空情况下均值-方差和均值-VaR投资组合比较研究[J].中国管理科学,2008,16(4):30-35.
[15] VapnikV. The Nature of Statistieal Leaming Theory [M]. NewYork Springer, 1995.
[16]应维云,覃正,赵宇等. SVM方法及其在客户流失预测中的应用研究[J].系统工程理论与实践, 2007,8(4):105-111.
[17]刘继海,陈晓剑. SVM模型在信用卡申请管理中的创新应用[J].哈尔滨工业大学学报(社会科学版),2007,9(4):133-136.
[18]姜明辉,袁绪川.个人信用评估PSO-SVM模型的构建及应用[J].管理学报,2008,5(4):511-515.
[19]郭雪松,孙林岩,徐晟.基于P-SVM的绿色供应商评价模型[J].预测,2007,26(5):7-11.
[20]胡达沙,王坤华.基于PSO和SVM的上市公司财务危机预警模型[J].管理学报,2007,4(5):588-592.
[21]李云飞,惠晓峰.基于支持向量机的股票投资价值分类模型研究[J].中国软科学, 2008,1:135-140.
[22]祝金荣.基于支持向量机的石油期货价格预测[J].工业技术经济,2007,26(2):59-61.
[23] Renata Mansini. Conditional value at risk and related linear programming models for portfolio optimization [J].Annals of Operations Research,2007,152(1):225-257.
[24] GJ Alexander,AM Baptista.A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model [J]. Management Science 2004, 50(9):1261-1273.
[25] Yongsheng Ding,Xinping Song and Yueming Zen. Forecasting financial condi-tion of Chinese listed companies based on support vector machine [J].ExpertSystems with Applications, 2008, 34(4): 3081-3089.
[26] Jae H. Min, Young-Chan Lee. Bankruptcy prediction using support vector machine with optimal choice of kernel function parameters [J]. Expert Systems with Applications, 2005, 28(4): 603-614.
[27] Akiko Taked and Takafumi Kanamori. A robust approach based on conditional value-at-risk measure to statistical learning Problems [J].European Journal of Operational Research, 2009, 198(1): 287-296.
[28] Michael Mainelli, Mark Yeandle. Best execution compliance: new techniques for managing compliance risk [J].The Journal of Risk Finance, 2006, 7(3): 301–312.
[29] JohnC P. Fast Training of Support Vector Machines using Sequential MinimalOptimization.Advances in Kernel Methods Support Vector Learning,CambridgeMA, MIT Press,1999:185-208.
[30] Keerthi S.Improvements to Platt’s SMO Algorithm for SVM Classier Design.National Uni. of Singapore, 1999.
[31] Mitra P,Murthy C.A, Pal.S.K.Data Condenstaion in Large Databases by Incre-metnal Learning with Support Vector Machines[C].In: Proceedings of ICPR2000,2000(2):712-715.
[32] L Wang,M Chang,J Feng.Citeseer Parallel and sequential support vector machines for multi-label classification [J]. International Journal of Information Te-chnology, 2005.
[33] Suykens J,Vadewalle J.Least Square Support Vector Machine Classifiers. Neu-ral Proeessing Letters.1999, 9(3):293-300.
[34] Paekard NH,Crutehfield JP, Farmer JD. Geometry from a time series [J]. Physical Review Letter.1989, 45(9):712-716.
[35]崔万照等.基于模糊模型支持向量机的混沌时间序列预测.物理学报.2005, 54(7):3009-3018.
[36]乔瑞F.风险价值VaR[M].陈跃,译.北京中信出版社,2005.
[37]龚锐,陈仲常,杨栋锐.GARCH族模型计算中国股市在险价值风险的比较研究与评述[J].数量经济技术经济研究, 2005(7):67-81.
[38] Vapnik V N.统计学习理论的本质[M].张学工译.北京:清华大学出版社,2000.
[39]张诏,张素,章琛曦,陈亚珠.基于支持向量机的概率密度估计方法[J].系统仿真学报,2005(17):2355-2357.
[40] P Morgan. Risk Metrics-Technical Document[R]. Fourth Edition. New-York, http://www.riskmetrics.com,1996.
[41] Kupiec P.Techniques for verifying the accuracy of risk measurement models [J]. Journal of Derivatives, 1995(3):73-84.
[2]严复,海党星,颜文虎.风险管理发展历程和趋势综述[J].管理现代化,2007(2): 30-33.
[3]肖志勇.VaR模型在金融风险管理中的应用[J].生产力研究,2008,2(4):44-46.
[4]秦拯,陈收,邹建军.VaR模型的计算方法及其评析[J].系统工程,2005,23(7):12-16.
[5]王玉玲.CVaR方法在投资组合中的应用[J].统计与决策,2008,2:71-72.
[6]徐元铖.国外风险价值模型研究现状[J].外国经济与管理,2005,27(6):44-51.
[7]周艳菊,邱菀华,王宗润.基于CVaR约束的多产品订货风险决策模型[J].中国管理科学,2006,14(5):62-67.
[8]孟志青,虞晓芬,蒋敏等.基于动态CVaR模型的房地产组合投资的风险度量与控制策略[J].系统工程理论与实践,2007,9:69-76.
[9]刘俊山.基于风险测度理论的VaR与CVaR的比较研究[J].数量经济技术经济研究,2007,3:125-133.
[10]蒋敏,胡奇英,孟志青.基于权值的多阶段风险值证券组合问题研究[J].管理工程学报,2006,20(3):38-40.
[11]刘小茂,杜红军.金融资产的VaR和CVaR风险的优良估计[J].中国管理科学,2006,14(5):1-6.
[12]杨磊,王明征,李文立.两种带有能力(Capacity)约束的报童风险模型最优策略[J].系统工程理论与实践,2008,5:35-42.
[13]韩国文.股票流动性风险测度模型的构建与实证分析[J].中国管理科学,2008,16(2):1-6.
[14]张鹏.不允许卖空情况下均值-方差和均值-VaR投资组合比较研究[J].中国管理科学,2008,16(4):30-35.
[15] VapnikV. The Nature of Statistieal Leaming Theory [M]. NewYork Springer, 1995.
[16]应维云,覃正,赵宇等. SVM方法及其在客户流失预测中的应用研究[J].系统工程理论与实践, 2007,8(4):105-111.
[17]刘继海,陈晓剑. SVM模型在信用卡申请管理中的创新应用[J].哈尔滨工业大学学报(社会科学版),2007,9(4):133-136.
[18]姜明辉,袁绪川.个人信用评估PSO-SVM模型的构建及应用[J].管理学报,2008,5(4):511-515.
[19]郭雪松,孙林岩,徐晟.基于P-SVM的绿色供应商评价模型[J].预测,2007,26(5):7-11.
[20]胡达沙,王坤华.基于PSO和SVM的上市公司财务危机预警模型[J].管理学报,2007,4(5):588-592.
[21]李云飞,惠晓峰.基于支持向量机的股票投资价值分类模型研究[J].中国软科学, 2008,1:135-140.
[22]祝金荣.基于支持向量机的石油期货价格预测[J].工业技术经济,2007,26(2):59-61.
[23] Renata Mansini. Conditional value at risk and related linear programming models for portfolio optimization [J].Annals of Operations Research,2007,152(1):225-257.
[24] GJ Alexander,AM Baptista.A comparison of VaR and CVaR constraints on portfolio selection with the mean-variance model [J]. Management Science 2004, 50(9):1261-1273.
[25] Yongsheng Ding,Xinping Song and Yueming Zen. Forecasting financial condi-tion of Chinese listed companies based on support vector machine [J].ExpertSystems with Applications, 2008, 34(4): 3081-3089.
[26] Jae H. Min, Young-Chan Lee. Bankruptcy prediction using support vector machine with optimal choice of kernel function parameters [J]. Expert Systems with Applications, 2005, 28(4): 603-614.
[27] Akiko Taked and Takafumi Kanamori. A robust approach based on conditional value-at-risk measure to statistical learning Problems [J].European Journal of Operational Research, 2009, 198(1): 287-296.
[28] Michael Mainelli, Mark Yeandle. Best execution compliance: new techniques for managing compliance risk [J].The Journal of Risk Finance, 2006, 7(3): 301–312.
[29] JohnC P. Fast Training of Support Vector Machines using Sequential MinimalOptimization.Advances in Kernel Methods Support Vector Learning,CambridgeMA, MIT Press,1999:185-208.
[30] Keerthi S.Improvements to Platt’s SMO Algorithm for SVM Classier Design.National Uni. of Singapore, 1999.
[31] Mitra P,Murthy C.A, Pal.S.K.Data Condenstaion in Large Databases by Incre-metnal Learning with Support Vector Machines[C].In: Proceedings of ICPR2000,2000(2):712-715.
[32] L Wang,M Chang,J Feng.Citeseer Parallel and sequential support vector machines for multi-label classification [J]. International Journal of Information Te-chnology, 2005.
[33] Suykens J,Vadewalle J.Least Square Support Vector Machine Classifiers. Neu-ral Proeessing Letters.1999, 9(3):293-300.
[34] Paekard NH,Crutehfield JP, Farmer JD. Geometry from a time series [J]. Physical Review Letter.1989, 45(9):712-716.
[35]崔万照等.基于模糊模型支持向量机的混沌时间序列预测.物理学报.2005, 54(7):3009-3018.
[36]乔瑞F.风险价值VaR[M].陈跃,译.北京中信出版社,2005.
[37]龚锐,陈仲常,杨栋锐.GARCH族模型计算中国股市在险价值风险的比较研究与评述[J].数量经济技术经济研究, 2005(7):67-81.
[38] Vapnik V N.统计学习理论的本质[M].张学工译.北京:清华大学出版社,2000.
[39]张诏,张素,章琛曦,陈亚珠.基于支持向量机的概率密度估计方法[J].系统仿真学报,2005(17):2355-2357.
[40] P Morgan. Risk Metrics-Technical Document[R]. Fourth Edition. New-York, http://www.riskmetrics.com,1996.
[41] Kupiec P.Techniques for verifying the accuracy of risk measurement models [J]. Journal of Derivatives, 1995(3):73-84.