中国股票市场的波动率聚集性研究——基于Markov机制转换Copula模型的实证分析
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摘要
波动率聚集性是金融资产收益率序列中的一个重要特征。构建了Markov机制转换Copula模型研究中国股票市场的波动率聚集性(波动率相关性结构)。采用上证综合指数和深证成份指数日内高频数据,构造已实现波动率作为隐波动率的代理变量,对中国股票市场进行了实证分析。结果表明,SJC Copula相比其他Copula能更好地刻画中国股票市场的波动率聚集性,波动率聚集具有明显的尾部非对称特征,高波动率的聚集相比低波动率的聚集发生概率要更高。另外,基于Markov机制转换SJC Copula模型的研究表明,中国股票市场的波动率聚集还具有明显的尾部动态特征。
Volatility clustering is one of the most important stylized facts in financial asset return series. This paper constructs the Markov regime switching copula model to study the volatility clustering(volatility dependence structure) in Chinese stock markets. Using the realized volatility constructed from the intraday high-frequency data as a proxy for the latent volatility, an empirical study of the Shanghai Stock Exchange composite index and the Shenzhen Stock Exchange component index of China is conducted. The empirical results demonstrate that the Symmetrized Joe Clayton(SJC) copula outperforms other copulas. The volatility clustering in Chinese stock markets exhibits asymmetric features in the sense that clusters of high volatility occur more often than clusters of low volatility. In addition, based on the results of the Markov regime switching SJC copula model, it is also found that the tail dependence of volatility clustering in Chinese stock markets exhibits a dynamic behavior.
Volatility clustering is one of the most important stylized facts in financial asset return series. This paper constructs the Markov regime switching copula model to study the volatility clustering(volatility dependence structure) in Chinese stock markets. Using the realized volatility constructed from the intraday high-frequency data as a proxy for the latent volatility, an empirical study of the Shanghai Stock Exchange composite index and the Shenzhen Stock Exchange component index of China is conducted. The empirical results demonstrate that the Symmetrized Joe Clayton(SJC) copula outperforms other copulas. The volatility clustering in Chinese stock markets exhibits asymmetric features in the sense that clusters of high volatility occur more often than clusters of low volatility. In addition, based on the results of the Markov regime switching SJC copula model, it is also found that the tail dependence of volatility clustering in Chinese stock markets exhibits a dynamic behavior.
引文
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[2] Bollerslev T. Generalized autoregressive conditional heteroskedasticity?[J]. Journal of Econometrics, 1986, 31: 307-327.
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[4] Lux T, Marchesi M. Volatility clustering in financial markets: A microsimulation of interacting agents[J]. International Journal of Theoretical and Applied Finance, 2000, 3(4): 675-702.
[5] Cont R. Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models[A]. In Handbook of Long Memory in Economics[C]//Berlin Heidelberg: Springer-Verlag, 2007.
[6] Gaunersdorfer A, Hommes C. A nonlinear structural model for volatility clustering[A]. In Handbook of Long Memory in Economics[C]//Berlin Heidelberg: Springer-Verlag, 2007.
[7] Jiang J, Li W, Cai X. Cluster behavior of a simple model in financial markets[J]. Physica A: Statistical Mechanics and its Applications, 2008, 387(2-3): 528-536.
[8] Tseng J J, Li S P. Asset returns and volatility clustering in financial time series[J]. Physica A: Statistical Mechanics and its Applications, 2011, 390(7): 1300-1314.
[9] Xue Y, Gencay R. Trading frequency and volatility clustering[J]. Journal of Banking & Finance, 2012, 36(3): 760-773.
[10] Stádník B. The riddle of volatility clusters[J]. Business: Theory and practice, 2014, 15(2): 140-148.
[11] Kumar R. Effect of volatility clustering on indifference pricing of options by convex risk measures[J]. Applied Mathematical Finance, 2015, 22(1): 63-82.
[12] Ning C, Xu D H, Wirjanto T S. Is volatility clustering of asset returns asymmetric?[J]. Journal of Banking & Finance, 2015, 52: 62-76.
[13] 易文德. 基于ARMA-GARCH-COUPULA模型的交易量与股价波动相依关系[J]. 系统管理学报, 2012, 21(5): 696-703.
[14] 吴亮, 庄亚明. 模糊随机环境下的单因子Gaussian Copula模型[J]. 系统管理学报, 2015, 24(4): 510-516.
[15] Patton A. Modelling asymmetric exchange rate dependence[J]. International Economic Review, 2006, 47: 527-556.
[16] 高岳, 王家华, 公彦德. 时变条件t-Copula蒙特卡罗方法的外汇储备收益风险度量[J]. 系统管理学报, 2012, 21(3): 319-326.
[17] Hafner C M, Reznikova O. Efficient estimation of a semiparametric dynamic Copula model[J]. Computational Statistics & Data Analysis, 2010, 54: 2609-2627.
[18] Hafner C M, Manner H. Dynamic stochastic Copula models: Estimation, inference and applications[J]. Journal of Applied Econometrics, 2012, 27: 269-295.
[19] Okimoto T. New evidence of asymmetric dependence structures in international equity markets[J]. Journal of Financial and Quantitative Analysis, 2008, 43: 787-816.
[20] Chollete L, Heinen A, Valdesogo A. Modeling international financial returns with a multivariate regime switching copula[J]. Journal of Financial Econometrics, 2009, 7: 437-480.
[21] Garcia R, Tsafack G. Dependence structure and extreme comovements in international equity and bond markets with portfolio diversification effects[J]. Journal of Banking and Finance, 2011, 35: 1954-1970.
[22] Manner H, Reznikova O. A survey on time-varying copulas: Specification, simulations, and application[J]. Econometric Reviews, 2012, 31(6): 654-687.
[23] Joe H. Multivariate models and dependence concepts[M]. London: Chapman & Hall, 1997.
[24] Patton A L. Copula-based models for financial time series[M]. In Handbook of Financial Time Series, Berlin Heidelberg: Springer-Verlag, 2009.
[25] Fermanian J D, Scaillet O. Some statistical pitfalls in copula modeling for financial applications[C]//In Klein E. Eds. Capital Formation, Governance and Banking. New York: Nova Science Publishing, 2005:59-74.
[26] 张连增, 胡祥. Copula的参数与半参数估计方法的比较[J]. 统计研究, 2014, 31(2): 91-95.
[27] Barndorff-Nielsen O E, Shephard N. Non-gaussian ornstein-ulhlenbeck-based models and some of their uses in fnancial economics[J]. Journal of the Royal Statistical Society, Series B, 2001, 63: 167-241.
[28] Hansen P R, Lunde A. A realized variance for the whole day based on intermittent high-frequency data[J]. Journal of Financial Econometrics, 2005, 3(4): 525-554.
[29] Engle R F. Risk and volatility: Econometric models and financial practice[J]. American Economic Review, 2004, 94(3): 405-420.
[30] Hamilton J. Time series analysis[M]. New Jersey: Princeton University Press, 1994.
[2] Bollerslev T. Generalized autoregressive conditional heteroskedasticity?[J]. Journal of Econometrics, 1986, 31: 307-327.
[3] Taylor S J. Financial returns modelled by the product of two stochastic processes —— A study of daily sugar prices[C]//In Anderson O D. Eds. Time Series Analysis: Theory and Practice 1. North Holland: Amsterdam, 1982:203-226.
[4] Lux T, Marchesi M. Volatility clustering in financial markets: A microsimulation of interacting agents[J]. International Journal of Theoretical and Applied Finance, 2000, 3(4): 675-702.
[5] Cont R. Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models[A]. In Handbook of Long Memory in Economics[C]//Berlin Heidelberg: Springer-Verlag, 2007.
[6] Gaunersdorfer A, Hommes C. A nonlinear structural model for volatility clustering[A]. In Handbook of Long Memory in Economics[C]//Berlin Heidelberg: Springer-Verlag, 2007.
[7] Jiang J, Li W, Cai X. Cluster behavior of a simple model in financial markets[J]. Physica A: Statistical Mechanics and its Applications, 2008, 387(2-3): 528-536.
[8] Tseng J J, Li S P. Asset returns and volatility clustering in financial time series[J]. Physica A: Statistical Mechanics and its Applications, 2011, 390(7): 1300-1314.
[9] Xue Y, Gencay R. Trading frequency and volatility clustering[J]. Journal of Banking & Finance, 2012, 36(3): 760-773.
[10] Stádník B. The riddle of volatility clusters[J]. Business: Theory and practice, 2014, 15(2): 140-148.
[11] Kumar R. Effect of volatility clustering on indifference pricing of options by convex risk measures[J]. Applied Mathematical Finance, 2015, 22(1): 63-82.
[12] Ning C, Xu D H, Wirjanto T S. Is volatility clustering of asset returns asymmetric?[J]. Journal of Banking & Finance, 2015, 52: 62-76.
[13] 易文德. 基于ARMA-GARCH-COUPULA模型的交易量与股价波动相依关系[J]. 系统管理学报, 2012, 21(5): 696-703.
[14] 吴亮, 庄亚明. 模糊随机环境下的单因子Gaussian Copula模型[J]. 系统管理学报, 2015, 24(4): 510-516.
[15] Patton A. Modelling asymmetric exchange rate dependence[J]. International Economic Review, 2006, 47: 527-556.
[16] 高岳, 王家华, 公彦德. 时变条件t-Copula蒙特卡罗方法的外汇储备收益风险度量[J]. 系统管理学报, 2012, 21(3): 319-326.
[17] Hafner C M, Reznikova O. Efficient estimation of a semiparametric dynamic Copula model[J]. Computational Statistics & Data Analysis, 2010, 54: 2609-2627.
[18] Hafner C M, Manner H. Dynamic stochastic Copula models: Estimation, inference and applications[J]. Journal of Applied Econometrics, 2012, 27: 269-295.
[19] Okimoto T. New evidence of asymmetric dependence structures in international equity markets[J]. Journal of Financial and Quantitative Analysis, 2008, 43: 787-816.
[20] Chollete L, Heinen A, Valdesogo A. Modeling international financial returns with a multivariate regime switching copula[J]. Journal of Financial Econometrics, 2009, 7: 437-480.
[21] Garcia R, Tsafack G. Dependence structure and extreme comovements in international equity and bond markets with portfolio diversification effects[J]. Journal of Banking and Finance, 2011, 35: 1954-1970.
[22] Manner H, Reznikova O. A survey on time-varying copulas: Specification, simulations, and application[J]. Econometric Reviews, 2012, 31(6): 654-687.
[23] Joe H. Multivariate models and dependence concepts[M]. London: Chapman & Hall, 1997.
[24] Patton A L. Copula-based models for financial time series[M]. In Handbook of Financial Time Series, Berlin Heidelberg: Springer-Verlag, 2009.
[25] Fermanian J D, Scaillet O. Some statistical pitfalls in copula modeling for financial applications[C]//In Klein E. Eds. Capital Formation, Governance and Banking. New York: Nova Science Publishing, 2005:59-74.
[26] 张连增, 胡祥. Copula的参数与半参数估计方法的比较[J]. 统计研究, 2014, 31(2): 91-95.
[27] Barndorff-Nielsen O E, Shephard N. Non-gaussian ornstein-ulhlenbeck-based models and some of their uses in fnancial economics[J]. Journal of the Royal Statistical Society, Series B, 2001, 63: 167-241.
[28] Hansen P R, Lunde A. A realized variance for the whole day based on intermittent high-frequency data[J]. Journal of Financial Econometrics, 2005, 3(4): 525-554.
[29] Engle R F. Risk and volatility: Econometric models and financial practice[J]. American Economic Review, 2004, 94(3): 405-420.
[30] Hamilton J. Time series analysis[M]. New Jersey: Princeton University Press, 1994.