基于Copula-GARCH的投资组合风险研究
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摘要
风险研究是一个内容极其广泛的领域,涵盖风险测度技术、相关性研究等。文章正是以相关关系为切入点,展开中国股票市场的组合风险研究。本文选取沪深港三市股票指数作为对象,具体内容包括：
理论方面,本文进行了风险管理相关理论的概述,主要介绍了风险计量技术(波动理论、风险测度模型)和联结理论(Copula)。 Copula理论是一种新的构建联合分布的方法,同时也是一种适用于探索非线性复杂相关关系的工具,目前已被广泛运用于金融领域。文章在深入介绍Copula理论的同时,提出了运用该方法进行投资组合的VaR计算。在计算VaR的过程中,采用的是蒙特卡洛模拟技术。
实证方面,文章分别针对沪深、沪港两市股票指数建立了Copula-GARCH模型,计算得到投资组合的市场风险,并采用蒙特卡洛模拟技术对模型的有效性进行验证。实证结果显示,三个市场的单市场波动情形适合采用具有尖峰厚尾假设分布的GARCH模型刻画；沪港和沪深两市之间体现出不同的相关关系：沪港之间适合使用Gumbel Copula,是一种上尾相关的关系,而沪深之间体现的则是一种上下尾对称的相关性,适合使用Frank Copula;沪港两市的等权重组合市场风险较小,优于沪深两市的等权重组合。
The study of risk refers to so many fields, such as risk measurement techniques, correlation research and so on. This article is about the portfolio risk research of china stock market, which takes the relevance as the breakthrough point. The paper bases on the Shanghai、 Shenzhen and Hong Kong share index:
Firstly, paper outlines theory of risk management:the risk measurement techniques (fluctuation theory, risk measure model) and coupling theory (Copula) in particular. Copula is an useful theory which can be implied to construct joint distribution and can explore non-linear relationship. The article puts forward to apply the theory to calculate VaR of portfolio, using the Monte Carlo simulation technology.
Secondly, paper does the empirical research of the return series by Copula-GARCH model and gets the portfolio market risk. The models used are proved to be valid by Monte Carlo simulation. Besides, other conclusions are:
GARCH model which has the assumption of t-distribution suits to sketch the fluctuation of single market. The relationships between them are different, Gumbel copula suits to shanghai-Hong Kong as the upper-tail correlation, while Frank copula for shanghai-Shenzhen as the symmetric correlation on upper and lower tail. Empirical research also suggests that the market risk combined by shanghai-Hong Kong is much smaller than combination of shanghai-Shenzhen.
理论方面,本文进行了风险管理相关理论的概述,主要介绍了风险计量技术(波动理论、风险测度模型)和联结理论(Copula)。 Copula理论是一种新的构建联合分布的方法,同时也是一种适用于探索非线性复杂相关关系的工具,目前已被广泛运用于金融领域。文章在深入介绍Copula理论的同时,提出了运用该方法进行投资组合的VaR计算。在计算VaR的过程中,采用的是蒙特卡洛模拟技术。
实证方面,文章分别针对沪深、沪港两市股票指数建立了Copula-GARCH模型,计算得到投资组合的市场风险,并采用蒙特卡洛模拟技术对模型的有效性进行验证。实证结果显示,三个市场的单市场波动情形适合采用具有尖峰厚尾假设分布的GARCH模型刻画；沪港和沪深两市之间体现出不同的相关关系：沪港之间适合使用Gumbel Copula,是一种上尾相关的关系,而沪深之间体现的则是一种上下尾对称的相关性,适合使用Frank Copula;沪港两市的等权重组合市场风险较小,优于沪深两市的等权重组合。
The study of risk refers to so many fields, such as risk measurement techniques, correlation research and so on. This article is about the portfolio risk research of china stock market, which takes the relevance as the breakthrough point. The paper bases on the Shanghai、 Shenzhen and Hong Kong share index:
Firstly, paper outlines theory of risk management:the risk measurement techniques (fluctuation theory, risk measure model) and coupling theory (Copula) in particular. Copula is an useful theory which can be implied to construct joint distribution and can explore non-linear relationship. The article puts forward to apply the theory to calculate VaR of portfolio, using the Monte Carlo simulation technology.
Secondly, paper does the empirical research of the return series by Copula-GARCH model and gets the portfolio market risk. The models used are proved to be valid by Monte Carlo simulation. Besides, other conclusions are:
GARCH model which has the assumption of t-distribution suits to sketch the fluctuation of single market. The relationships between them are different, Gumbel copula suits to shanghai-Hong Kong as the upper-tail correlation, while Frank copula for shanghai-Shenzhen as the symmetric correlation on upper and lower tail. Empirical research also suggests that the market risk combined by shanghai-Hong Kong is much smaller than combination of shanghai-Shenzhen.
引文
[1]Engle, Robert F. Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation. Econometrica, 1982, 50:987-1008
[2]Bollerslev, Tim. Generalized Autoregressive Conditonal Heteroskedasticity. Journal of Econometrics,1986,31:307-327
[3]Nelson, D.B. Conditional Heteroskedasticity in Asset Returns:A New Approach. Econometrica,1991,59:347-370
[4]Taylor S J. Modeling Financial Time Series [M].Chichester:John Wiley and Sons,1986
[5]Schwert, G.W. Why Does Stock Market Volatility Change over Time? Journal of Finance,1989,54:1115-1151
[6]Ding Zhuangxin, C.W.J,Granger and R.f.Engle. A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance,1993, 1:83-106
[7]Glosten, L., R, Jafannathan, and D.Runkle,. On the relations between the expected value and the volatility on the nominal excess returns on stocks[J]. Journal of Finance,1993,48:1779-1801
[8]Zakoian J.M. Threshold Heteroskedastic Models. Journal of Economic Dynamics and Control,1994,18:931-944
[9]Glosten,L.R., Jagannathan and D.Runkle. On the Relation between the Expected Value and the Volatility of the Norminal Excess Return on Stocks. Journal of Finance,1993,48:1779-1801
[10]McNeil, A.J. and Frey. R. Estimation of tail-related risk measures for heteroscedastic financial time series:an extreme value approach, Journal of Empirical Finance 2000,7:271-300
[11]P.Verhoeven, M.McAleer Fat tails and asymmetry in financial volatility models. Mathematics and Computers in Simulation,2004,64:351-361
[12]陈守东,俞世典.基于GARCH模型的VaR方法对中国股市的分析[J].吉林大学社会科学学报,2002年4期
[13]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究.金融研究,2002年第5期
[14]朱永安,曲春青.上海股票市场两阶段波动非对称性实证研究[J].统计与信息论坛,2003年04期
[15]梁建,康宇虹.信托介入风险投资的主要方式[N].金融时报,2002年第15期
[16]朱慧明,曾慧芳,曹英.基于MCMC模拟的贝叶斯AR-GJR-GARCH模型及其应用.统计与决策,2008年第02期
[17]Sklar A. Functions de Repartition do Dimensions Etlures Merges [J]. Publ Inst Statist of Paris University,1959,8:229-231
[18]Nelsen R B. An Introduction to Copulas [M]. New York:Springer Press, 1999
[19]Embrechts P, Lindskog F, McNeil A. Modeling dependence with copulas and applications to risk management. 2001:145-156
[20]Li D.X. On Default Correlation:A Copula Function Approach. Journal of Fixed Income,2000,9:43-54
[21]Ane Thierry, Kharoubi Cecile. Dependence Structure and Risk Measure. The Journal of Business.2003.76:30
[22]Rockinger,M. & Jondeau,E. Conditional Dependency of Financial Series: An Application of Copulas.2001
[23]Patton, Andrew J. Estimation of Copula Models for Time Series of Possibly Different Length.2001
[24]Di Clemente A.Romano C. Measuring Portfolio Value-at-Risk by a Copula-EVT Based Approach[R].Rome:University of Rome La Sapienza, 2003
[25]Yasuhiro Yamai Toshinao Yoshiba. Value-at-risk versus expected shortfall:A practical perspective. Journal of Banking Finance,294 997-1015
[26]Rockinger,M. and E.Jondeau. The Copula-GARCH Model of Conditional Dependencies:An International Stock Market Applicaition. Journal of International Money and Finance, 2001.5:827-853
[27]张尧庭.连接函数(Copula)技术与金融风险分析[J].统计研究,2002年第4期
[28]韦艳华,张世英.金融市场的相关性分析——Copula-GARCH模型及其应用[J].系统工程,2004年04期
[29]刘志东.基于Copula-GARCH-EVT的资产组合选择模型及其混合遗传算法[J].系统工程理论方法应用,2006年02期
[30]陈守东,胡铮洋Copula函数度量风险价值的Monte Carlo模拟[J].吉林大学社会科学学报,2006年第3期
[31]朱世武.基于Copula的VaR度量与事后检验.数理统计与管,2007年第6期
[32]韦艳华,张世英Copula理论及其在金融分析上的应用[Z].清华大学出版社.2008
[33]John C. Hull, Alan White. Incorporating volatility updating into the historical simulation method for VaR. The Journal of Risk. 1998.1:5-19
[34]Martin Martens. Testing the mixture of distributions hypothesis using "realized" volatility
[35]郑文通.金融风险管理的VaR方法及其应用[J].国际金融研究,1997年第9期
[36]马杰.人民币行为研究与外汇风险管理.2001
[37]陈学华,杨辉耀VaR-APARCH模型与证券投资风险量化分析.中国管理科学,2003年01期
[38]尹念.基于VAR方法的我国股市风险管理实证研究.湖南财经高等专科学校学报,2010年26卷5期
[39]张田.VAR方法在某大型外贸企业风险管理中的应用.经济视角,2010年03期
[40]R T.Rockafeller, S.Uryasev. Optimization of conditional value at risk. The Journal of Risk.2000.2(3):21-41
[41]刘小茂,李楚霖,王建华.风险资产组合的均值-CVaR有效前沿(I)[J].管理工程学报,2003年01期
[42]曲圣宁,田新时.投资组合风险管理中VaR模型的缺陷以及CVaR模型研究[J].统计与决策,2005年10期
[43]曹志鹏,王晓芳.基于CVaR的我国银行间债券回购市场利率[J].财经问题研究,2008年第11期
[44]E Bouye. Copulas:An Open Field for Risk Management.2001
[45]Jean-Frederic Jouanin. Financial Applications of Copula Functions. Risk Measure for 21st century. Par Giorgio Szego, ed., John Wiley & Sons, 2004
[46]Christian Cech. Copula-Based Top-Down Approaches in Financial Risk Aggregation
[47]吴庆晓,刘海龙,许友传.重尾分布下的期望收益风险度量方法[J].上海交通大学学报,2009年04期
[48]侯成琪,王频.基于连接函数的整合风险度量研究.统计研究,2008年第 11期
[49]肖振宇,胡挺.金融控股集团风险管理：基于Copula-VaR分析.统计与决策(理论版),2007年第7期
[50]霍光耀,郭名媛.金融波动研究的新进展及未来展望.经济学·管理学研究
[51]汪办兴.中国银行业全面风险管理改进研究[D].复旦大学.2007年
[52]李平,马婷婷.基于Copula的我国商业银行整体风险度量[J].硅谷,2008年12期
[2]Bollerslev, Tim. Generalized Autoregressive Conditonal Heteroskedasticity. Journal of Econometrics,1986,31:307-327
[3]Nelson, D.B. Conditional Heteroskedasticity in Asset Returns:A New Approach. Econometrica,1991,59:347-370
[4]Taylor S J. Modeling Financial Time Series [M].Chichester:John Wiley and Sons,1986
[5]Schwert, G.W. Why Does Stock Market Volatility Change over Time? Journal of Finance,1989,54:1115-1151
[6]Ding Zhuangxin, C.W.J,Granger and R.f.Engle. A Long Memory Property of Stock Market Returns and a New Model. Journal of Empirical Finance,1993, 1:83-106
[7]Glosten, L., R, Jafannathan, and D.Runkle,. On the relations between the expected value and the volatility on the nominal excess returns on stocks[J]. Journal of Finance,1993,48:1779-1801
[8]Zakoian J.M. Threshold Heteroskedastic Models. Journal of Economic Dynamics and Control,1994,18:931-944
[9]Glosten,L.R., Jagannathan and D.Runkle. On the Relation between the Expected Value and the Volatility of the Norminal Excess Return on Stocks. Journal of Finance,1993,48:1779-1801
[10]McNeil, A.J. and Frey. R. Estimation of tail-related risk measures for heteroscedastic financial time series:an extreme value approach, Journal of Empirical Finance 2000,7:271-300
[11]P.Verhoeven, M.McAleer Fat tails and asymmetry in financial volatility models. Mathematics and Computers in Simulation,2004,64:351-361
[12]陈守东,俞世典.基于GARCH模型的VaR方法对中国股市的分析[J].吉林大学社会科学学报,2002年4期
[13]陈浪南,黄杰鲲.中国股票市场波动非对称性的实证研究.金融研究,2002年第5期
[14]朱永安,曲春青.上海股票市场两阶段波动非对称性实证研究[J].统计与信息论坛,2003年04期
[15]梁建,康宇虹.信托介入风险投资的主要方式[N].金融时报,2002年第15期
[16]朱慧明,曾慧芳,曹英.基于MCMC模拟的贝叶斯AR-GJR-GARCH模型及其应用.统计与决策,2008年第02期
[17]Sklar A. Functions de Repartition do Dimensions Etlures Merges [J]. Publ Inst Statist of Paris University,1959,8:229-231
[18]Nelsen R B. An Introduction to Copulas [M]. New York:Springer Press, 1999
[19]Embrechts P, Lindskog F, McNeil A. Modeling dependence with copulas and applications to risk management. 2001:145-156
[20]Li D.X. On Default Correlation:A Copula Function Approach. Journal of Fixed Income,2000,9:43-54
[21]Ane Thierry, Kharoubi Cecile. Dependence Structure and Risk Measure. The Journal of Business.2003.76:30
[22]Rockinger,M. & Jondeau,E. Conditional Dependency of Financial Series: An Application of Copulas.2001
[23]Patton, Andrew J. Estimation of Copula Models for Time Series of Possibly Different Length.2001
[24]Di Clemente A.Romano C. Measuring Portfolio Value-at-Risk by a Copula-EVT Based Approach[R].Rome:University of Rome La Sapienza, 2003
[25]Yasuhiro Yamai Toshinao Yoshiba. Value-at-risk versus expected shortfall:A practical perspective. Journal of Banking Finance,294 997-1015
[26]Rockinger,M. and E.Jondeau. The Copula-GARCH Model of Conditional Dependencies:An International Stock Market Applicaition. Journal of International Money and Finance, 2001.5:827-853
[27]张尧庭.连接函数(Copula)技术与金融风险分析[J].统计研究,2002年第4期
[28]韦艳华,张世英.金融市场的相关性分析——Copula-GARCH模型及其应用[J].系统工程,2004年04期
[29]刘志东.基于Copula-GARCH-EVT的资产组合选择模型及其混合遗传算法[J].系统工程理论方法应用,2006年02期
[30]陈守东,胡铮洋Copula函数度量风险价值的Monte Carlo模拟[J].吉林大学社会科学学报,2006年第3期
[31]朱世武.基于Copula的VaR度量与事后检验.数理统计与管,2007年第6期
[32]韦艳华,张世英Copula理论及其在金融分析上的应用[Z].清华大学出版社.2008
[33]John C. Hull, Alan White. Incorporating volatility updating into the historical simulation method for VaR. The Journal of Risk. 1998.1:5-19
[34]Martin Martens. Testing the mixture of distributions hypothesis using "realized" volatility
[35]郑文通.金融风险管理的VaR方法及其应用[J].国际金融研究,1997年第9期
[36]马杰.人民币行为研究与外汇风险管理.2001
[37]陈学华,杨辉耀VaR-APARCH模型与证券投资风险量化分析.中国管理科学,2003年01期
[38]尹念.基于VAR方法的我国股市风险管理实证研究.湖南财经高等专科学校学报,2010年26卷5期
[39]张田.VAR方法在某大型外贸企业风险管理中的应用.经济视角,2010年03期
[40]R T.Rockafeller, S.Uryasev. Optimization of conditional value at risk. The Journal of Risk.2000.2(3):21-41
[41]刘小茂,李楚霖,王建华.风险资产组合的均值-CVaR有效前沿(I)[J].管理工程学报,2003年01期
[42]曲圣宁,田新时.投资组合风险管理中VaR模型的缺陷以及CVaR模型研究[J].统计与决策,2005年10期
[43]曹志鹏,王晓芳.基于CVaR的我国银行间债券回购市场利率[J].财经问题研究,2008年第11期
[44]E Bouye. Copulas:An Open Field for Risk Management.2001
[45]Jean-Frederic Jouanin. Financial Applications of Copula Functions. Risk Measure for 21st century. Par Giorgio Szego, ed., John Wiley & Sons, 2004
[46]Christian Cech. Copula-Based Top-Down Approaches in Financial Risk Aggregation
[47]吴庆晓,刘海龙,许友传.重尾分布下的期望收益风险度量方法[J].上海交通大学学报,2009年04期
[48]侯成琪,王频.基于连接函数的整合风险度量研究.统计研究,2008年第 11期
[49]肖振宇,胡挺.金融控股集团风险管理：基于Copula-VaR分析.统计与决策(理论版),2007年第7期
[50]霍光耀,郭名媛.金融波动研究的新进展及未来展望.经济学·管理学研究
[51]汪办兴.中国银行业全面风险管理改进研究[D].复旦大学.2007年
[52]李平,马婷婷.基于Copula的我国商业银行整体风险度量[J].硅谷,2008年12期