金融市场间波动溢出效应研究——基于Gumber的二维CARR模型和生存Copula-CARR模型
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摘要
基于Gumber的二维指数分布,建立了Gumber的二维CARR模型,采用极大似然估计的两步法,以上证极差序列和深证极差序列为样本,考查了在极端情形下金融市场之间的波动溢出,并与CCC-GARCH模型进行比较,发现Gumber的二维CARR模型的估计更符合实际,能捕捉在极端情况下的波动溢出效应。利用蒙特卡洛方法进行了模拟和分析,进一步证实Gumber的二维CARR模型能合理有效地测度波动溢出效应。最后,对Gumber的二维CARR模型进行了扩展,在CARR模型中引入生存Copula函数,构建了生存Copula-CARR模型,进而建立了一种新的刻画金融波动溢出效应的多维CARR模型。
A Gumber's two-dimensional CARR model is established first based on Gumber's twodimensional exponent distribution. Under the model, the volatility spillover under extreme circumstances is examined, by two-step estimation of maximum likelihood, between Shanghai Stock Market and Shenzhen Stock Market in range series. Compared with CCC-GARCH model, the results from the Gumber's two-dimensional CARR model agree more with the actual situation, can capture volatility spillover in extreme cases. The Monte Carlo method is then applied to simulate, analyze, and further verify that the Gumber's two-dimensional CARR model can reasonably and effectively measure volatility spillover.Finally, with the survival copulas function involved, the Gumber's two-dimensional CARR model is developed into the survival copula-CARR model, a new multidimensional CARR model, which can examine the volatility spillover of multiple financial markets.
A Gumber's two-dimensional CARR model is established first based on Gumber's twodimensional exponent distribution. Under the model, the volatility spillover under extreme circumstances is examined, by two-step estimation of maximum likelihood, between Shanghai Stock Market and Shenzhen Stock Market in range series. Compared with CCC-GARCH model, the results from the Gumber's two-dimensional CARR model agree more with the actual situation, can capture volatility spillover in extreme cases. The Monte Carlo method is then applied to simulate, analyze, and further verify that the Gumber's two-dimensional CARR model can reasonably and effectively measure volatility spillover.Finally, with the survival copulas function involved, the Gumber's two-dimensional CARR model is developed into the survival copula-CARR model, a new multidimensional CARR model, which can examine the volatility spillover of multiple financial markets.
引文
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[3] Harvey A C, Shephard N. Estimation of an asymmetric stochastic variance model for asset returns[J]. Journal of Business and Economic Statistics, 1996, 14(2):429-434.
[4] Miyakoshi T. Spillovers of stock return volatility to Asian equity markets from Japan and the US[J]. Journal of International Financial Markets Institutional and Money, 2006, 13(3):383-399.
[5] Cho J H, Parhizgari A M. East Asian financial contagion under DCC-GARCH[J]. International Journal of Banking and Finance, 2008, 6(1):17-30.
[6] Tsiaplias S, Chua C L. A multivariate GARCH model incorporating the direct and indirect transmission of Shocks[J]. Ecnometric Reviews, 2013, 32(2):244-271.
[7] Hai V T. Tsui A K, Zhang Z. Measuring asymmetry and persistence in conditional volatility in real output:evidence from three East Asian tigers using a multivariate GARCH approach[J]. Applied Economics, 2013, 45(20):2909-2914.
[8]方毅.国内外期铜价格之间的长期记忆成分和短期波动溢出效应[J].数理统计与管理,2008, 27(2):304-312.
[9]熊正德,韩丽君.基于MSV类模型的中国汇市与股市间溢出效应[J].系统工程,2010,(10):47-53.
[10]曹广喜,崔维军,韩彦.人民币汇率弹性调整对我国汇市与股市关系的影响一基于长记忆VAR-(BEKK)MVGARCH模型[J].数理统计与管理,2014, 33(6):1101-1112.
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[12]袁晨,傅强,彭选华.我国股票与债券、黄金间的资产组合功能研究一基于DCC-MVGARCH模型的动态相关性分析[J].数理统计与管理,2014, 33(4):714-723.
[13]颜斌斌,田立平,刘洪伟.沪铜期货与现货市场的价格发现与波动溢出效应[J].数学的实践与认识,2016,(2):114-120.
[14]鲁思瑶,徐美萍.基于扭曲混合Copula和ARMA-GARCH-t模型的投资组合风险分析一以上证综指、中证综合债和上证基金为例[J].数理统计与管理,2017, 36(6):1131-1140.
[15]徐国祥,周昀.中国外汇市场压力指数与货币政策关联性一基于TVP-VAR方法的实证分析[J].数理统计与管理,2017, 36(2):313-325.
[16] Chou R Y. Forecasting financial volatilities with extreme values:The conditional autoregressive range(CARR)model[J]. Journal of Money Credit and Banking, 2005, 37(3):561-582.
[17]耿立艳,马军海.运用最小二乘支持向量回归机和CARRX模型对股市波动率的预测[J].统计与决策,2008,(13):48-50.
[18] Geng L Y, Zhang Z F. CARRX model based on LSSVR optimized by adaptive PSO[J]. Digital Manufacturing and Automation(ICDMA), 2012, 5(65):268-271.
[19]赵树然,任培民,赵昕.基于CARR-EVT整体方法的动态日VaR和CVaR模型研究[J].数量经济技术经济研究,2012,(11):130-148.
[20] Sin C. Using CARRX models to study factors affecting the volatilities of Asian equity markets[J].North American Journal of Economics&Finance, 2013, 26(4):552-564.
[21]郭名媛,蒲赢健.基于ACARR模型的布伦特原油价格波动研究[J].重庆理工大学学报(自然科学版),2016, 30(3):51-56.
[22]王沁.基于杠杆效应CARR模型的波动率预测[J].数理统计与管理,2017, 36(1):51-58.
[23]蒲赢健.基于Copula-CARR模型的原油价格与汇率相关性分析和波动溢出研究[D].天津大学,2016.
[24] Gumbel E J. Bivariate exponential distributions[J]. Journal of the American Statistical Association,1960, 52(292):698-707.
[25] Freund J E. A bivariate extension of the exponential distribution[J]. Journal of the American Statistical Association, 1961, 56(7):971-977.
[26] Kolokolov A. Hedging with futures:Multivariate dynamic conditional correlation GARCH[J]. Market Risk and Financial Markets Modeling, 2012, 4:63-72.
[27] Newey W K, McFadden D. Large Sample Estimation and Hypothesis Testing, in Handbook of Econometrics[M]. North-Holland, Elsevier, 1994.
[28] Sklar A, Schweizer B. Probabilistic Metric Space[M]. New York:North-holland, 1983.
[29] Genest C, Mackay J. The joy of copulas:Bivariate distributions with uniform marginal[J]. The American Statistician, 1986, 40:280-283.
[30]张瑞锋,张世英,唐勇.金融市场波动溢出分析及实证研究[J].中国管理科学,2006, 14(5):14-22.
[31]陈碟.聚合相依风险极端事件的渐近性状[D].中国科学技术大学,2013.
[2] Harvey A C, Ruiz E, Shephard N. Multivariate stochastic variance model[J]. The Reviews of Economic Studies, 1994, 61(2):247-264.
[3] Harvey A C, Shephard N. Estimation of an asymmetric stochastic variance model for asset returns[J]. Journal of Business and Economic Statistics, 1996, 14(2):429-434.
[4] Miyakoshi T. Spillovers of stock return volatility to Asian equity markets from Japan and the US[J]. Journal of International Financial Markets Institutional and Money, 2006, 13(3):383-399.
[5] Cho J H, Parhizgari A M. East Asian financial contagion under DCC-GARCH[J]. International Journal of Banking and Finance, 2008, 6(1):17-30.
[6] Tsiaplias S, Chua C L. A multivariate GARCH model incorporating the direct and indirect transmission of Shocks[J]. Ecnometric Reviews, 2013, 32(2):244-271.
[7] Hai V T. Tsui A K, Zhang Z. Measuring asymmetry and persistence in conditional volatility in real output:evidence from three East Asian tigers using a multivariate GARCH approach[J]. Applied Economics, 2013, 45(20):2909-2914.
[8]方毅.国内外期铜价格之间的长期记忆成分和短期波动溢出效应[J].数理统计与管理,2008, 27(2):304-312.
[9]熊正德,韩丽君.基于MSV类模型的中国汇市与股市间溢出效应[J].系统工程,2010,(10):47-53.
[10]曹广喜,崔维军,韩彦.人民币汇率弹性调整对我国汇市与股市关系的影响一基于长记忆VAR-(BEKK)MVGARCH模型[J].数理统计与管理,2014, 33(6):1101-1112.
[11]王雪标,周维利,范庆珍.我国原油价格与外国原油价格的波动溢出效应一基于DCC-MGARCH模型分析[J].数理统计与管理,2012, 31(4):571-584.
[12]袁晨,傅强,彭选华.我国股票与债券、黄金间的资产组合功能研究一基于DCC-MVGARCH模型的动态相关性分析[J].数理统计与管理,2014, 33(4):714-723.
[13]颜斌斌,田立平,刘洪伟.沪铜期货与现货市场的价格发现与波动溢出效应[J].数学的实践与认识,2016,(2):114-120.
[14]鲁思瑶,徐美萍.基于扭曲混合Copula和ARMA-GARCH-t模型的投资组合风险分析一以上证综指、中证综合债和上证基金为例[J].数理统计与管理,2017, 36(6):1131-1140.
[15]徐国祥,周昀.中国外汇市场压力指数与货币政策关联性一基于TVP-VAR方法的实证分析[J].数理统计与管理,2017, 36(2):313-325.
[16] Chou R Y. Forecasting financial volatilities with extreme values:The conditional autoregressive range(CARR)model[J]. Journal of Money Credit and Banking, 2005, 37(3):561-582.
[17]耿立艳,马军海.运用最小二乘支持向量回归机和CARRX模型对股市波动率的预测[J].统计与决策,2008,(13):48-50.
[18] Geng L Y, Zhang Z F. CARRX model based on LSSVR optimized by adaptive PSO[J]. Digital Manufacturing and Automation(ICDMA), 2012, 5(65):268-271.
[19]赵树然,任培民,赵昕.基于CARR-EVT整体方法的动态日VaR和CVaR模型研究[J].数量经济技术经济研究,2012,(11):130-148.
[20] Sin C. Using CARRX models to study factors affecting the volatilities of Asian equity markets[J].North American Journal of Economics&Finance, 2013, 26(4):552-564.
[21]郭名媛,蒲赢健.基于ACARR模型的布伦特原油价格波动研究[J].重庆理工大学学报(自然科学版),2016, 30(3):51-56.
[22]王沁.基于杠杆效应CARR模型的波动率预测[J].数理统计与管理,2017, 36(1):51-58.
[23]蒲赢健.基于Copula-CARR模型的原油价格与汇率相关性分析和波动溢出研究[D].天津大学,2016.
[24] Gumbel E J. Bivariate exponential distributions[J]. Journal of the American Statistical Association,1960, 52(292):698-707.
[25] Freund J E. A bivariate extension of the exponential distribution[J]. Journal of the American Statistical Association, 1961, 56(7):971-977.
[26] Kolokolov A. Hedging with futures:Multivariate dynamic conditional correlation GARCH[J]. Market Risk and Financial Markets Modeling, 2012, 4:63-72.
[27] Newey W K, McFadden D. Large Sample Estimation and Hypothesis Testing, in Handbook of Econometrics[M]. North-Holland, Elsevier, 1994.
[28] Sklar A, Schweizer B. Probabilistic Metric Space[M]. New York:North-holland, 1983.
[29] Genest C, Mackay J. The joy of copulas:Bivariate distributions with uniform marginal[J]. The American Statistician, 1986, 40:280-283.
[30]张瑞锋,张世英,唐勇.金融市场波动溢出分析及实证研究[J].中国管理科学,2006, 14(5):14-22.
[31]陈碟.聚合相依风险极端事件的渐近性状[D].中国科学技术大学,2013.
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