VaR在中国证券投资风险管理中的应用
摘要
VaR作为已发展较为完善的风险测量方法,同时也是国际金融监管工具,现在正逐步的全面引入我国金融机构。VaR方法本身既能简单清晰的表示市场风险的大小,又有严谨系统的概率统计理论作为依托,能够以直观的数字为投资者提供可以理解的风险评估衡量。有鉴于中国股市巨大的波动性与居民风险投资意识的薄弱,笔者希望通过自身对VaR的学习与掌握,构架一套简陋却完整的VaR方法体系,并将它应用于股票市场指数的分析之中,可以为人所参考。本文就目前比较流行的风险控制技术VaR在我国的证券投资风险控制中的应用进行介绍和研究,并结合我国证券市场的现状进行实证研究和分析,期望通过比较研究选出较为适合我国股指样本特点的VaR的计算方法,为我国广大的非金融机构投资者和中小散户投资者,特别是为中小散户投资者提供量化证券投资风险控制的工具.
本文主要研究了GARCH类模型、极值理论、EWMA算法和核估计在动态VaR计算中的应用,并对其中的EWMA算法在算法上和衰减因子的选择方法进行了改进和比较.笔者选用上证180指数作为实证研究的对象,将最新的截止到09年4月的收盘指数数据纳入考察范围。在使用Eviews5.0系统的分析了其对数收益率序列的统计分布特征的基础上,对序列的最小二乘估计残差进行了ARCH效应检验.借助MATLAB完成了对使用GARCH类模型、极值理论进行的VaR计算.
在EWMA算法中,笔者创新性的提出尝试使用样本内数据依照VaR回测中的Kupiec似然比检验来选取适合的衰减因子λ,取代以往依照估计的方差尽可能的接近γ~2的原则确定λ.另外,笔者对EWMA算法中的零均值假设提出质疑,提出了对条件均值的非零假设并与零均值假设下的EWMA算法进行比较,证明在短期内存在较大的连续下跌势头时,均值的引入可以更加保守的给出VaR,而且在现有样本下的实证研究取得了很好的效果,笔者对这一结果的成因进行了分析.
在引入核估计的历史模拟法中,受改进EWMA算法时,应用EMWA模型下的迭代法算出条件均值的启发,将给日收益率赋权的权重设为使用衰减因子为λ的按历史时间指数衰减,并与未加权的核估计方法进行比较,比较结果证明,加权核估计的综合表现显著优于未赋权的核估计方法。
As a method which has been developed completely,VaR is also the tool for international financial supervision and management.Nowadays,it has been used in our country's financial agencies.Moreover,the VaR method can denote the market risk intuitively while based on the theories of probability and statistics.In this way,VaR points a figure simply for the risk hiding in the financial products.In view of the huge volatility in China's stock market,the author attempt to construct a simple VaR System and take it into application for the analysis of stock index.This article introduces the application of some modish VaR method in our country's securities market.Those methods are applied into the Shanghai Stock Exchange 180 Index for empirical research and comparative.And the author just hope to choose the one which is the most suitable for the sample of China's stock market for common use.
In the article,we focus on the application of GARCH model,Extreme Value Theory, the algorithm of EWMA and Kernel estimation in dynamic VaR calculation.And the improvement of EWMA algorithm was raised.The Shanghai Stock Exchange 180 Index is choosed for empirical study while we used the close index up to April,2009 which is the latest.The character of the return rate series' distribution is analysised by Eviews 5.0,and the test for ARCH effection is taken as well.Matlab is taken into the estimating of VaR in GARCH model and Extreme Value Theory.
When it comes to the algorithm of EWMA,the author attempts to find a suitableλthrough the Kupiec likelihood ratio test for the in-the-sample data.The non-zero assumption is taken into the condition mean to improve the EWMA algorithm.And it is proved that the new method makes a better performance in the choosed sample.
The Kernel estimation is taken into historical simulation method,we try to use the exponentially weighted rate replace the real rate of return before estimation.And this is proved to performance better.
本文主要研究了GARCH类模型、极值理论、EWMA算法和核估计在动态VaR计算中的应用,并对其中的EWMA算法在算法上和衰减因子的选择方法进行了改进和比较.笔者选用上证180指数作为实证研究的对象,将最新的截止到09年4月的收盘指数数据纳入考察范围。在使用Eviews5.0系统的分析了其对数收益率序列的统计分布特征的基础上,对序列的最小二乘估计残差进行了ARCH效应检验.借助MATLAB完成了对使用GARCH类模型、极值理论进行的VaR计算.
在EWMA算法中,笔者创新性的提出尝试使用样本内数据依照VaR回测中的Kupiec似然比检验来选取适合的衰减因子λ,取代以往依照估计的方差尽可能的接近γ~2的原则确定λ.另外,笔者对EWMA算法中的零均值假设提出质疑,提出了对条件均值的非零假设并与零均值假设下的EWMA算法进行比较,证明在短期内存在较大的连续下跌势头时,均值的引入可以更加保守的给出VaR,而且在现有样本下的实证研究取得了很好的效果,笔者对这一结果的成因进行了分析.
在引入核估计的历史模拟法中,受改进EWMA算法时,应用EMWA模型下的迭代法算出条件均值的启发,将给日收益率赋权的权重设为使用衰减因子为λ的按历史时间指数衰减,并与未加权的核估计方法进行比较,比较结果证明,加权核估计的综合表现显著优于未赋权的核估计方法。
As a method which has been developed completely,VaR is also the tool for international financial supervision and management.Nowadays,it has been used in our country's financial agencies.Moreover,the VaR method can denote the market risk intuitively while based on the theories of probability and statistics.In this way,VaR points a figure simply for the risk hiding in the financial products.In view of the huge volatility in China's stock market,the author attempt to construct a simple VaR System and take it into application for the analysis of stock index.This article introduces the application of some modish VaR method in our country's securities market.Those methods are applied into the Shanghai Stock Exchange 180 Index for empirical research and comparative.And the author just hope to choose the one which is the most suitable for the sample of China's stock market for common use.
In the article,we focus on the application of GARCH model,Extreme Value Theory, the algorithm of EWMA and Kernel estimation in dynamic VaR calculation.And the improvement of EWMA algorithm was raised.The Shanghai Stock Exchange 180 Index is choosed for empirical study while we used the close index up to April,2009 which is the latest.The character of the return rate series' distribution is analysised by Eviews 5.0,and the test for ARCH effection is taken as well.Matlab is taken into the estimating of VaR in GARCH model and Extreme Value Theory.
When it comes to the algorithm of EWMA,the author attempts to find a suitableλthrough the Kupiec likelihood ratio test for the in-the-sample data.The non-zero assumption is taken into the condition mean to improve the EWMA algorithm.And it is proved that the new method makes a better performance in the choosed sample.
The Kernel estimation is taken into historical simulation method,we try to use the exponentially weighted rate replace the real rate of return before estimation.And this is proved to performance better.
引文
[1]菲利普.乔瑞著.陈跃等译.风险价值VAR.中信出版社,2005年1月.
[2]汪洋.金融市场风险管理.VaR模型的应用.复旦大学,2003年12月.
[3]刘艳春、高立群、王珂.基于GARCH模型的VaR计算.中国控制与决策学术年会论文集,2005年.
[4]王雨飞、王宇平.基于遗传算法的CVaR模型.中国管理科学,2006年10月.
[5]邵伟文.VaR体系的发展研究与改进.中国科学院,2003年1月.
[6]胡婷.VaR方法在证券投资基金风险管理中的应用研究.华中科技大学,2004年4月.
[7]姚娜.VaR模型在中国股市风险管理中的应用研究.西北大学,2007年6月.
[8]吴晓滨.VAR-GARCH方法在证券投资风险管理中的运用.中国人民银行金融研究所,2007年4月.
[9]Nelson Daniel B.Conditional Heterosdasticity in Asset Returns:A New Appreach.Econometrica,1991,59:347-370.
[10]Hendricks D.Evaluation of Value-at-Risk Models Using Historical Data.Economic Policy Review,Federal Reserve Bank of New York 2(April 1996),39 -69.
[11]王春峰.金融市场管理.天津大学出版社,2002年4月.
[12]Butler S J&Schachter B.Estimating Value at Risk with precision measure by combining kernel estimation with historical simulation.Review of Derivatives Research,l:371-390,1998.
[13]Ding Z,Granger,C.W.J.,Engle,R.F.A Long Memory Property of Stock Market Returns and a New Model.Journal of Empirical Finance,Vol.1,83-106,1993.
[14]Embrechts.P,Resnick.S&Samorodnitsky,G.Exterme value theory as a risk management tool.Manuscript.Zurich,Switzerland:Department of Mathematics,ETH,Swiss Federal Technical University.1998.
[15]Embrechts.P.Extreme value theory in finance and insurance.Manuscript.Zurich,Switzerland:Department of Mathematics,ETH,Swiss Federal Technical University.1999.
[16]Embrechts.P.Extreme value theory:Potentials and limitations as an integrated risk management tool.Manuscript.Zurich,Switzerland:Department of Mathematics,ETH,Swiss Federal Technical University.2000.
[17]Engle.R&M.Gizycki.Conservatism,Accuracy and Efficiency:Comparing Value-at-Risk Models.Working Paper 2,Match,1999.
[18]E ngle.R&C.Manganlli.Conditional Autoregressive Value at Risk:CAVaR Models.WorkingPaper,Department of Economics,University of California,San Diego.1999.
[19]Guermat.C&Harris R.D.F.Robust Conditional Variance Estimation and Value-at-Risk.Journal of Risk,4(2),25-41.2001.
[20]Guermat.C&Harris R.D.F.Forecasting value at risk allowing for time variation in the variance and kurtosis of portfolio returns.International Journal of Forecasting 18,pp 409-419.2002.
[21]Hull.John&White.Alan.Incorporating Volatility Updating into the Historical Simulation Method for Value-at-Risk.Journal of Risk 1,5-19.2002年4月.
[22]J.P.Morgan.Risk Metrics Technical Document fourth edition.New York.1996
[23]Kupiec P.H.Techniques for verifying the accuracy of risk measurement models.The Journal of Derivatives,3(2):73-84.1995.
[24]McNeil.A.J.Estimating the tails of loss severity distributions using extreme value theory.ASTIN Bulletin,27,1117-1137.1997.
[25]McNeil.A.J&Frey.R.Estimation of tail-related risk measures for heteroscedastic financial time series:An extreme value approach..Journal of Empirical Finance,7,271-300.2000.
[26]Silverman.B.Density Estimation for Statistics and Data Analysis.London:Chapman and Hall.1986.
[2]汪洋.金融市场风险管理.VaR模型的应用.复旦大学,2003年12月.
[3]刘艳春、高立群、王珂.基于GARCH模型的VaR计算.中国控制与决策学术年会论文集,2005年.
[4]王雨飞、王宇平.基于遗传算法的CVaR模型.中国管理科学,2006年10月.
[5]邵伟文.VaR体系的发展研究与改进.中国科学院,2003年1月.
[6]胡婷.VaR方法在证券投资基金风险管理中的应用研究.华中科技大学,2004年4月.
[7]姚娜.VaR模型在中国股市风险管理中的应用研究.西北大学,2007年6月.
[8]吴晓滨.VAR-GARCH方法在证券投资风险管理中的运用.中国人民银行金融研究所,2007年4月.
[9]Nelson Daniel B.Conditional Heterosdasticity in Asset Returns:A New Appreach.Econometrica,1991,59:347-370.
[10]Hendricks D.Evaluation of Value-at-Risk Models Using Historical Data.Economic Policy Review,Federal Reserve Bank of New York 2(April 1996),39 -69.
[11]王春峰.金融市场管理.天津大学出版社,2002年4月.
[12]Butler S J&Schachter B.Estimating Value at Risk with precision measure by combining kernel estimation with historical simulation.Review of Derivatives Research,l:371-390,1998.
[13]Ding Z,Granger,C.W.J.,Engle,R.F.A Long Memory Property of Stock Market Returns and a New Model.Journal of Empirical Finance,Vol.1,83-106,1993.
[14]Embrechts.P,Resnick.S&Samorodnitsky,G.Exterme value theory as a risk management tool.Manuscript.Zurich,Switzerland:Department of Mathematics,ETH,Swiss Federal Technical University.1998.
[15]Embrechts.P.Extreme value theory in finance and insurance.Manuscript.Zurich,Switzerland:Department of Mathematics,ETH,Swiss Federal Technical University.1999.
[16]Embrechts.P.Extreme value theory:Potentials and limitations as an integrated risk management tool.Manuscript.Zurich,Switzerland:Department of Mathematics,ETH,Swiss Federal Technical University.2000.
[17]Engle.R&M.Gizycki.Conservatism,Accuracy and Efficiency:Comparing Value-at-Risk Models.Working Paper 2,Match,1999.
[18]E ngle.R&C.Manganlli.Conditional Autoregressive Value at Risk:CAVaR Models.WorkingPaper,Department of Economics,University of California,San Diego.1999.
[19]Guermat.C&Harris R.D.F.Robust Conditional Variance Estimation and Value-at-Risk.Journal of Risk,4(2),25-41.2001.
[20]Guermat.C&Harris R.D.F.Forecasting value at risk allowing for time variation in the variance and kurtosis of portfolio returns.International Journal of Forecasting 18,pp 409-419.2002.
[21]Hull.John&White.Alan.Incorporating Volatility Updating into the Historical Simulation Method for Value-at-Risk.Journal of Risk 1,5-19.2002年4月.
[22]J.P.Morgan.Risk Metrics Technical Document fourth edition.New York.1996
[23]Kupiec P.H.Techniques for verifying the accuracy of risk measurement models.The Journal of Derivatives,3(2):73-84.1995.
[24]McNeil.A.J.Estimating the tails of loss severity distributions using extreme value theory.ASTIN Bulletin,27,1117-1137.1997.
[25]McNeil.A.J&Frey.R.Estimation of tail-related risk measures for heteroscedastic financial time series:An extreme value approach..Journal of Empirical Finance,7,271-300.2000.
[26]Silverman.B.Density Estimation for Statistics and Data Analysis.London:Chapman and Hall.1986.