iVIX指数与上证50 ETF收益率的相关性实证研究
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摘要
采用1分钟高频数据,研究i VIX指数与上证50 ETF收益率之间的相关性。运用参数估计和核密度估计描述两者的边缘分布,通过K-S拟合优度检验构建Copula模型。研究表明:Copula模型具有较好的拟合优度,Copula函数相对于Kendall和Spearman分析方法不仅能够捕捉i VIX指数与ETF收益率序列间的秩相关性,而且还能反映i VIX指数与ETF收益率的尾部相关性; i VIX指数与上证50 ETF收益率之间存在负的秩相关性,秩相关性强弱随着不同持有期大致呈现"W"型分布,通过Copula概率密度函数的尾部相关性发现i VIX指数与ETF收益率存在非对称结构特征。
This paper uses the 1mins high frequency data of China Volatility index( i VIX) and return of Shanghai Stock Exchange Traded Fund( SSE) to study the correlation between them. Nonparametric kernel density estimator and parameter estimation are used to describe the exponential edge distribution. Copula model is tested by K-S method. The research shows that the copula indicates the goodness of fit. Compared with the traditional Kendall and Spearman correlation analysis,the copula model can not only capture the rank correlation between i VIX index and the return of SSE,but also reflects the tail correlation between them. The negative rank correlation shows W-shaped distribution during different holding periods. Through the tail correlation of Copula's probability density function,it shows that the i VIX index and the return of SSE have asymmetric characteristics.
This paper uses the 1mins high frequency data of China Volatility index( i VIX) and return of Shanghai Stock Exchange Traded Fund( SSE) to study the correlation between them. Nonparametric kernel density estimator and parameter estimation are used to describe the exponential edge distribution. Copula model is tested by K-S method. The research shows that the copula indicates the goodness of fit. Compared with the traditional Kendall and Spearman correlation analysis,the copula model can not only capture the rank correlation between i VIX index and the return of SSE,but also reflects the tail correlation between them. The negative rank correlation shows W-shaped distribution during different holding periods. Through the tail correlation of Copula's probability density function,it shows that the i VIX index and the return of SSE have asymmetric characteristics.
引文
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[14]Nguyen C,Bhatti M I,KomorníkováM,et al.Gold price and stock markets nexus under mixed-copulas[J].Economic Modelling,2016,58:283-292.
[15]任仙玲,叶明确,张世英.基于Copula-APD-GARCH模型的投资组合有效前沿分析[J].管理学报,2009,6(11):1528-1535.
[16]吴玉宝,汪金菊.沪深股市的相关结构分析与投资组合风险度量---基于ARFIMA-GARCH-Copula模型[J].运筹与管理,2016,25(2):220-225.
[17]Bollen N P B,O'Neill M J,Whaley R E.Tail Wags Dog:Intraday Price Discovery in VIX Markets[J].Journal of Futures Markets,2017.37(5):431-451.
[18]Kao D X,Tsai W C,Wang Y H,et al.An analysis on the intraday trading activity of VIX derivatives[J].Journal of Futures Markets,2018,38(2):158-174.
[19]Scaillet O,Fermanian J D.Nonparametric Estimation of Copulas for Time Series[J].Fame Research Paper,2003,5(4):189-196.
[20]任仙玲,张世英.基于核估计及多元阿基米德Copula的投资组合风险分析[J].管理科学,2007,20(5):92-96.
[21]Schweizer B,Wolff E F.On Nonparametric Measures of Dependence for Random Variables[J].Annals of Statistics,1981,9(4):879-885.
[22]郑振龙,汤文玉.波动率风险及风险价格---来自中国A股市场的证据[J].金融研究,2011(4):143-157.
[23]林树,俞乔.有限理性、动物精神及市场崩溃:对情绪波动与交易行为的实验研究[J].经济研究,2010(8):115-127.
[24]蔡庆丰,宋友勇.超常规发展的机构投资者能稳定市场吗?---对我国基金业跨越式发展的反思[J].经济研究,2010(1):90-101.
[25]李志文,余佩琨,杨靖.机构投资者与个人投资者羊群行为的差异[J].金融研究,2010(11):77-89.
[2]Fleming J.The quality of market volatility forecasts implied by S&P 100 index option prices[J].Journal of Empirical Finance,1998,5(4):317-345.
[3]Fleming J,Ostdiek B,Whaley R E.Predicting stock market volatility:A new measure[J].Journal of Futures Markets,1995,15(3):265-302.
[4]Christensen B J,Prabhala N R.The relation between implied and realized volatility[J].Journal of Financial Economics,1998,50(2):125-150.
[5]Giot P.Implied volatility indexes and daily Value at Risk models[J].The Journal of derivatives,2005,12(4):54-64.
[6]Giot P.Relationships between implied volatility indexes and stock index returns[J].The Journal of Portfolio Management,2005,31(3):92-100.
[7]Ang A,Hodrick R J,Xing Y,et al.The cross-section of volatility and expected returns[J].The Journal of Finance,2006,61(1):259-299.
[8]Goldwhite P.Diversification and risk management:What volatility tells us[J].The Journal of Investing,2009,18(3):40-48.
[9]Qadan M,Cohen G.Is it profitable to invest according to the VIX fear index[J].Journal of Modern Accounting and Auditing,2011,7(1):86-90.
[10]Chandra A,Thenmozhi M.On asymmetric relationship of India volatility index(India VIX)with stock market return and risk management[J].Decision,2015,42(1):33-55.
[11]Sklar A.Fonctions de répartitionàn dimensions et leurs marges.Publications de l’Institut de Statistique de l’Universitéde Paris[J].1959,8:229-231.
[12]Patton A J.Modelling asymmetric exchange rate dependence[J].International economic review,2006,47(2):527-556.
[13]魏平,刘海生.Copula模型在沪深股市相关性研究中的应用[J].数理统计与管理,2010,29(5):890-898.
[14]Nguyen C,Bhatti M I,KomorníkováM,et al.Gold price and stock markets nexus under mixed-copulas[J].Economic Modelling,2016,58:283-292.
[15]任仙玲,叶明确,张世英.基于Copula-APD-GARCH模型的投资组合有效前沿分析[J].管理学报,2009,6(11):1528-1535.
[16]吴玉宝,汪金菊.沪深股市的相关结构分析与投资组合风险度量---基于ARFIMA-GARCH-Copula模型[J].运筹与管理,2016,25(2):220-225.
[17]Bollen N P B,O'Neill M J,Whaley R E.Tail Wags Dog:Intraday Price Discovery in VIX Markets[J].Journal of Futures Markets,2017.37(5):431-451.
[18]Kao D X,Tsai W C,Wang Y H,et al.An analysis on the intraday trading activity of VIX derivatives[J].Journal of Futures Markets,2018,38(2):158-174.
[19]Scaillet O,Fermanian J D.Nonparametric Estimation of Copulas for Time Series[J].Fame Research Paper,2003,5(4):189-196.
[20]任仙玲,张世英.基于核估计及多元阿基米德Copula的投资组合风险分析[J].管理科学,2007,20(5):92-96.
[21]Schweizer B,Wolff E F.On Nonparametric Measures of Dependence for Random Variables[J].Annals of Statistics,1981,9(4):879-885.
[22]郑振龙,汤文玉.波动率风险及风险价格---来自中国A股市场的证据[J].金融研究,2011(4):143-157.
[23]林树,俞乔.有限理性、动物精神及市场崩溃:对情绪波动与交易行为的实验研究[J].经济研究,2010(8):115-127.
[24]蔡庆丰,宋友勇.超常规发展的机构投资者能稳定市场吗?---对我国基金业跨越式发展的反思[J].经济研究,2010(1):90-101.
[25]李志文,余佩琨,杨靖.机构投资者与个人投资者羊群行为的差异[J].金融研究,2010(11):77-89.