基于GARCH族模型的沪深300股指VaR度量
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摘要
本文在修正了沪深300股票指数收益率序列的非平稳性和自身相关性之后,把ARMA模型与GARCH模型、GJR模型、IGARCH模型、FIGARCH模型、FIEGARCH模型、FIAPARCH模型、HYGARCH模型相结合,然后依次假设残差分布服从正态分布、t分布和偏t分布,来描述沪深300股票指数日对数收益率序列的尖峰厚尾性、杠杆效应和长记忆特性,利用上述模型分别计算沪深300股票指数的VaR值.在空头和多头投资者情况下,不同的波动性模型和不同残差分布的VaR预测有效性差距很大.比较得知,在不同的置信水平下,沪深300股票指数收益率序列空头和多头的VaR预测成功概率比较高的模型有HYGARCH和FIEGARCH这两类具有长记忆性的模型.
In this paper we firstly try to characterize the sharp peak and fat tail phenomena,leverage effects and long memory features of the logarithmic returns of the Shanghai and Shenzhen 300( HS 300) stock indexes by using the ARMA model to describe the means and the 7 models: the GARCH model,the GJR model,the IGARCH model,the FIGARCH model,the FIEGARCH model,the FIAPARCH model and the HYGARCH model,to respectively fit the residual sequences which are assumed sequently to follow a normal distribution,a t distribution or a skewed t distribution,and then use those models to forecast the VaR of the HS 300 stock indexes. The empirical results show that the forecasts of the VaR with different models of volatilities and residual distributions in short and long cases differ greatly,and it is concluded by comparison that,at different confidence levels,the HYGARCH and the FIEGARCH models which are more suitable for characterizing long memory features have more accuracy for forecasting the VaR of the HS 300 stock indexes.
In this paper we firstly try to characterize the sharp peak and fat tail phenomena,leverage effects and long memory features of the logarithmic returns of the Shanghai and Shenzhen 300( HS 300) stock indexes by using the ARMA model to describe the means and the 7 models: the GARCH model,the GJR model,the IGARCH model,the FIGARCH model,the FIEGARCH model,the FIAPARCH model and the HYGARCH model,to respectively fit the residual sequences which are assumed sequently to follow a normal distribution,a t distribution or a skewed t distribution,and then use those models to forecast the VaR of the HS 300 stock indexes. The empirical results show that the forecasts of the VaR with different models of volatilities and residual distributions in short and long cases differ greatly,and it is concluded by comparison that,at different confidence levels,the HYGARCH and the FIEGARCH models which are more suitable for characterizing long memory features have more accuracy for forecasting the VaR of the HS 300 stock indexes.
引文
[1]姜全,刘孟.HS300指数收益波动性及VaR度量研究[J].金融经济,2008(08):87-89
[2]陈德华,石建民.我国证券市场风险波动性预测:基于沪深300指数的比较研究[J].生产力研究,2009(4):36-38.
[3]马超群,李红权,周恩,杨晓光,徐山鹰,张银旗.风险价值方法及其实证研究[J].中国管理科学,2001,9(5):16-23.
[4]田宏伟,詹原瑞,邱军.极值理论(EVT)方法用于受险价值(VaR)计算的实证比较与分析[J].系统工程理论与实践,2000,10:27-35.
[5]樊智,张世英.金融波动性及实证研究[J].中国管理科学,2002,10(6):27-30.
[6]王春峰,张庆翠.中国股市波动性过程中的长期记忆性实证研究[J].系统工程,2004,22(1):78-83.
[7]赵进文,王倩.上证180指数的GARCH族模型仿真研究—对上证300指数的间接实证建模分析[J].财经问题研究,2008(3):47-52.
[8]仝玉民.股票市场波动性—来自沪深300指数的证据[J].金融经济,2009(6):81-83.
[9]高可佑,王潇怡,黄勇兵.沪深300指数的VaR风险测量—基于历史模拟和蒙特卡罗模拟法[J].金融观察,2008(3):90-91.
[10]林宇,魏宇,黄登仕.基于GJR模型的EVT动态风险测度研究.系统工程学报,2008(2):45-51.
[11]肖智,傅肖肖,钟波.基于EVT-POT-FIGARCH的动态VaR风险测度[J].南开管理评论,2008(4):100-104.
[12]肖智,傅肖肖,钟波.基于EVT-BM-FIGARCH的动态VaR风险测度[J].中国管理科学,2008(8):19-23.
[13]周孝华,唐秋燕.沪深300指数极值VaR的分析与计算[J].统计与决策,2008(10):96-98.
[14]严定琪,李育锋.基于GARCH族模型的沪深300指数波动率预测[J].兰州交通大学学报,2008(2):92-95.
[15]章辉,胡颖,骆媛媛等.沪深股指期货的保证金设计—基于“分形市场”假说的研究[J].财贸经济,2008(4):36-41.
[16]马守业,赵昕.基于极值理论的证券市场VaR实证研究[J].中共青岛市委党校青岛行政学院学报,2008(11):39-41.
[17]金丹.沪深300指数的ARCH效应[J].湖北经济学院学报,2008(2):47-50.
[18]Alexander J.M.Rudiger F.Estimation of tail-related risk measures for heteroscedastic financial time series:an extreme value approach[J].Journal of Empirical Finance,2000(7):271-300.
[19]Baillie RT,Bollerslev TMIK Kelsen HO.Fractionally integrated generalized autoregressive conditional heteroskedasticity[J].Journal of Econometrics,1996:3-30.
[20]Malay Bhattacharyya,Gopal Ritolia.Conditional VaR using EVT—Towards a planned Margin scheme[J].International Review of Financial Analysis,2006,doi:10 1016/j irfa 2006 08 004.
[21]Ping-Tsung Wu,Shwu-Jane Shieh.Value-at-Risk analysis for long-term interest rate futures:Fattail and long memory in return innovations[J].Journal of Empirical Finance,2007,14:248-259.
[22]Chris Brooks and Gita Persand.The Effect of Asymmetries on Stock Index Return Value at Risk Estimates[J].Journal of Risk Finance,2003,4(2):29-421.
[23]Wolfgang Karl Hardle.Value-at-Risk and Expected Shortfall when there is long range dependence[J].SFB649 Discussion Paper,2008-006.
[24]Aktham I.Maghyereh.The tail behavior of extreme stock returns in the Gulf emerging markets[J].Studies in Economics and Finance,2008(1):21-37.
[2]陈德华,石建民.我国证券市场风险波动性预测:基于沪深300指数的比较研究[J].生产力研究,2009(4):36-38.
[3]马超群,李红权,周恩,杨晓光,徐山鹰,张银旗.风险价值方法及其实证研究[J].中国管理科学,2001,9(5):16-23.
[4]田宏伟,詹原瑞,邱军.极值理论(EVT)方法用于受险价值(VaR)计算的实证比较与分析[J].系统工程理论与实践,2000,10:27-35.
[5]樊智,张世英.金融波动性及实证研究[J].中国管理科学,2002,10(6):27-30.
[6]王春峰,张庆翠.中国股市波动性过程中的长期记忆性实证研究[J].系统工程,2004,22(1):78-83.
[7]赵进文,王倩.上证180指数的GARCH族模型仿真研究—对上证300指数的间接实证建模分析[J].财经问题研究,2008(3):47-52.
[8]仝玉民.股票市场波动性—来自沪深300指数的证据[J].金融经济,2009(6):81-83.
[9]高可佑,王潇怡,黄勇兵.沪深300指数的VaR风险测量—基于历史模拟和蒙特卡罗模拟法[J].金融观察,2008(3):90-91.
[10]林宇,魏宇,黄登仕.基于GJR模型的EVT动态风险测度研究.系统工程学报,2008(2):45-51.
[11]肖智,傅肖肖,钟波.基于EVT-POT-FIGARCH的动态VaR风险测度[J].南开管理评论,2008(4):100-104.
[12]肖智,傅肖肖,钟波.基于EVT-BM-FIGARCH的动态VaR风险测度[J].中国管理科学,2008(8):19-23.
[13]周孝华,唐秋燕.沪深300指数极值VaR的分析与计算[J].统计与决策,2008(10):96-98.
[14]严定琪,李育锋.基于GARCH族模型的沪深300指数波动率预测[J].兰州交通大学学报,2008(2):92-95.
[15]章辉,胡颖,骆媛媛等.沪深股指期货的保证金设计—基于“分形市场”假说的研究[J].财贸经济,2008(4):36-41.
[16]马守业,赵昕.基于极值理论的证券市场VaR实证研究[J].中共青岛市委党校青岛行政学院学报,2008(11):39-41.
[17]金丹.沪深300指数的ARCH效应[J].湖北经济学院学报,2008(2):47-50.
[18]Alexander J.M.Rudiger F.Estimation of tail-related risk measures for heteroscedastic financial time series:an extreme value approach[J].Journal of Empirical Finance,2000(7):271-300.
[19]Baillie RT,Bollerslev TMIK Kelsen HO.Fractionally integrated generalized autoregressive conditional heteroskedasticity[J].Journal of Econometrics,1996:3-30.
[20]Malay Bhattacharyya,Gopal Ritolia.Conditional VaR using EVT—Towards a planned Margin scheme[J].International Review of Financial Analysis,2006,doi:10 1016/j irfa 2006 08 004.
[21]Ping-Tsung Wu,Shwu-Jane Shieh.Value-at-Risk analysis for long-term interest rate futures:Fattail and long memory in return innovations[J].Journal of Empirical Finance,2007,14:248-259.
[22]Chris Brooks and Gita Persand.The Effect of Asymmetries on Stock Index Return Value at Risk Estimates[J].Journal of Risk Finance,2003,4(2):29-421.
[23]Wolfgang Karl Hardle.Value-at-Risk and Expected Shortfall when there is long range dependence[J].SFB649 Discussion Paper,2008-006.
[24]Aktham I.Maghyereh.The tail behavior of extreme stock returns in the Gulf emerging markets[J].Studies in Economics and Finance,2008(1):21-37.