基于Levy-GARCH模型的上证50ETF市场跳跃行为与波动特征研究
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摘要
上证ETF50期权的发行推动学界开始关注其标的资产的波动特点。本文引入带跳跃的Levy-GARCH非高斯条件异方差模型,结合Fourier数值极大似然估计及回溯测试,对上证50ETF的跳跃和波动特征进行实证分析,并与上证综指、深证成指进行比较。研究结果表明,与国内主要市场指数相比,上证50ETF市场同样存在显著的条件异方差效应和随机跳跃行为,但波动率并不存在显著的杠杆效应。本文通过与多个市场和行业指数进行对照比较,并从行业特征、成份股特征、市场机制特点等角度解释了上证50ETF杠杆效应不显著的原因。
Volatility is one of the significant features of the capital market.It is important to characterize the volatility of financial markets accurately which plays an important role in effective risk management and rational derivatives pricing.ETF50 option listing begins to attract wide attention from academics to focus on the volatility features of underlying assets.Therefore,in order to study the random jump behavior and the volatility features of Shanghai 50 ETF market,non-Gaussian Levy-GARCH model is introduced,such as Merton jump diffusion model,combined with maximum likelihood estimate with Fast Fourier and back testing,compared with Shanghai composite index and Shenzhen composite index,to analyze volatility features of Shanghai 50 ETF market.Return series of several markets in China during the period of 2005 to2016 are investigated.Research results show that fat tail,long memory,clustering effect,conditional heteroskedasticity and random jump behavior are well reflected in Shanghai 50 ETF market,meanwhile,leverage effect does not exist.For exploring reasons why this phenomenon exists,the analysis will be presented in the following aspects:industry characteristics,features of constituent stocks and market mechanism.These researches will contribute to further development about the issue of derivatives pricing and risk management based on open-end funds.
Volatility is one of the significant features of the capital market.It is important to characterize the volatility of financial markets accurately which plays an important role in effective risk management and rational derivatives pricing.ETF50 option listing begins to attract wide attention from academics to focus on the volatility features of underlying assets.Therefore,in order to study the random jump behavior and the volatility features of Shanghai 50 ETF market,non-Gaussian Levy-GARCH model is introduced,such as Merton jump diffusion model,combined with maximum likelihood estimate with Fast Fourier and back testing,compared with Shanghai composite index and Shenzhen composite index,to analyze volatility features of Shanghai 50 ETF market.Return series of several markets in China during the period of 2005 to2016 are investigated.Research results show that fat tail,long memory,clustering effect,conditional heteroskedasticity and random jump behavior are well reflected in Shanghai 50 ETF market,meanwhile,leverage effect does not exist.For exploring reasons why this phenomenon exists,the analysis will be presented in the following aspects:industry characteristics,features of constituent stocks and market mechanism.These researches will contribute to further development about the issue of derivatives pricing and risk management based on open-end funds.
引文
[1]陈浪南.波动率研究[M].北京:中国财政经济出版社,2008.
[2]刘国光,王慧敏.基于纯粹跳跃利维过程的中外股票收益分布特征研究[J].数理统计与管理,2006,25(1):43-46.
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[4]黄苒,唐齐鸣.基于可变强度跳跃-GARCH模型的资产价格跳跃行为分析---以中国上市公司股票市场数据为例[J].中国管理科学,2014,22(6):1-9.
[5]赵华.中国股市的跳跃性与杠杆效应---基于已实现极差方差的研究[J].金融研究,2012,(11):179-192.
[6]胡志军,沈根祥.中国股市资产的价格跳跃行为---基于上证综指、深证成指的高频数据研究[J].上海经济研究,2013,(4):88-99.
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[15]Engle R F,Ng V K.Measuring and Testing the impact of news on volatility[J].The Journal of Finance,1993,48(5):1749-1778.
[16]董铁牛,杨乃定,姜继娇,等.中国开放式基金市场波动性的实证研究[J].管理工程学报,2008,22(3):134-137.
[17]Xie Shiqing,Huang Xichen.An empirical analysis of the volatility in the open-end fund market:Evidence from China[J].Emerging Markets Finance and Trade,2013,49(4):150-162.
[18]韩超.基于GARCH模型的上证50指数收益率波动性分析[J].金融经济月刊,2015,(6):161-163.
[19]Schoutens W.Levy processes in finance[M].New York:John Wiley&Sons,Ltd,2003.
[20]吴恒煜,朱福敏,胡根华,等.基于参数学习的GARCH动态无穷活动率Levy过程的欧式期权定价[J].系统工程理论与实践,2014,(10):2465-2482.
[21]贾馨云,苏应生,高春燕.VaR模型在股市风险分析中的应用及实证分析[J].中国管理科学,2014,(s1):336-341.
[22]吴鑫育,李心丹,马超群.门限已实现随机波动率模型及其实证研究[J].中国管理科学,2017,25(3):10-19.
[23]Rodríguez M J,Ruiz E.Revisiting several popular GARCH models with leverage effect:Differences and similarities[J].Journal of Financial Econometrics,2012,10(4):637-668.
[24]Andersen T G,Benzoni L,Lund J.An empirical investigation of continuous-time equity return models[J].Journal of Finance,2002,57(3):1239-1284.
[25]Jacquier E,Polson N G,Rossi P E.Bayesian analysis of stochastic volatility models with fat-tails and correlated errors[J].Journal of Econometrics,2004,122(1):185-212.
[26]王春.投资者情绪对股票市场收益和波动的影响-基于开放式股票型基金资金净流入的实证研究[J].中国管理科学,2014,22(9):49-56.
[27]杨炘,王小征,滕召学.中国股市个人与机构投资者的羊群效应[J].清华大学学报(自然科学版),2004,44(12):1610-1614.
[28]刘志东,严冠.基于半鞅过程的中国股市随机波动、跳跃和微观结构噪声统计特征研究[J].中国管理科学,2016,24(05):18-30.
[29]杨胜刚.行为金融、噪声交易与中国证券市场主体行为特征研究[J].经济评论,2002(4):83-85.
[2]刘国光,王慧敏.基于纯粹跳跃利维过程的中外股票收益分布特征研究[J].数理统计与管理,2006,25(1):43-46.
[3]陈国进,王占海.我国股票市场连续性波动与跳跃性波动实证研究[J].系统工程理论与实践,2010,30(9):1554-1562.
[4]黄苒,唐齐鸣.基于可变强度跳跃-GARCH模型的资产价格跳跃行为分析---以中国上市公司股票市场数据为例[J].中国管理科学,2014,22(6):1-9.
[5]赵华.中国股市的跳跃性与杠杆效应---基于已实现极差方差的研究[J].金融研究,2012,(11):179-192.
[6]胡志军,沈根祥.中国股市资产的价格跳跃行为---基于上证综指、深证成指的高频数据研究[J].上海经济研究,2013,(4):88-99.
[7]Merton R C.Option pricing when underlying stock returns are discontinuous[J].Journal of Financial Economics,1975,3(1):125-144.
[8]Kou S G.A jump-diffusion model for option pricing[J].Management Science,2002,48(8):1086-1101.
[9]Madan D B,Seneta E.The variance gamma model for share market returns[J].Journal of Business,1990,63(4):511-524.
[10]Barndorff-Nielsen O E.Processes of normal inverse gaussian type[J].Finance and Stochastics,1998,2(1):41-68.
[11]Carr P,Grman H,Madan D B,et al.The fine structure of asset returns:An empirical investigation[J].Journal of Business,2002,75(2):305-332.
[12]Engle R F.Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation[J].The Econometric Society,1982,50(4):987-1007.
[13]Bollerslev T.Generalized autoregressive conditional heteroskedasticity[J].Journal of Econometrics,1986,31(3):307-327.
[14]Nelson D B.Conditional heteroskedasticity in asset returns:A new approach[J].The Econometric Society,1991,59(2):347-370.
[15]Engle R F,Ng V K.Measuring and Testing the impact of news on volatility[J].The Journal of Finance,1993,48(5):1749-1778.
[16]董铁牛,杨乃定,姜继娇,等.中国开放式基金市场波动性的实证研究[J].管理工程学报,2008,22(3):134-137.
[17]Xie Shiqing,Huang Xichen.An empirical analysis of the volatility in the open-end fund market:Evidence from China[J].Emerging Markets Finance and Trade,2013,49(4):150-162.
[18]韩超.基于GARCH模型的上证50指数收益率波动性分析[J].金融经济月刊,2015,(6):161-163.
[19]Schoutens W.Levy processes in finance[M].New York:John Wiley&Sons,Ltd,2003.
[20]吴恒煜,朱福敏,胡根华,等.基于参数学习的GARCH动态无穷活动率Levy过程的欧式期权定价[J].系统工程理论与实践,2014,(10):2465-2482.
[21]贾馨云,苏应生,高春燕.VaR模型在股市风险分析中的应用及实证分析[J].中国管理科学,2014,(s1):336-341.
[22]吴鑫育,李心丹,马超群.门限已实现随机波动率模型及其实证研究[J].中国管理科学,2017,25(3):10-19.
[23]Rodríguez M J,Ruiz E.Revisiting several popular GARCH models with leverage effect:Differences and similarities[J].Journal of Financial Econometrics,2012,10(4):637-668.
[24]Andersen T G,Benzoni L,Lund J.An empirical investigation of continuous-time equity return models[J].Journal of Finance,2002,57(3):1239-1284.
[25]Jacquier E,Polson N G,Rossi P E.Bayesian analysis of stochastic volatility models with fat-tails and correlated errors[J].Journal of Econometrics,2004,122(1):185-212.
[26]王春.投资者情绪对股票市场收益和波动的影响-基于开放式股票型基金资金净流入的实证研究[J].中国管理科学,2014,22(9):49-56.
[27]杨炘,王小征,滕召学.中国股市个人与机构投资者的羊群效应[J].清华大学学报(自然科学版),2004,44(12):1610-1614.
[28]刘志东,严冠.基于半鞅过程的中国股市随机波动、跳跃和微观结构噪声统计特征研究[J].中国管理科学,2016,24(05):18-30.
[29]杨胜刚.行为金融、噪声交易与中国证券市场主体行为特征研究[J].经济评论,2002(4):83-85.