针对共同跳跃研究的不足,文章沿袭已有理论框架,采用常用的日内跳跃检验方法,构建了共同跳跃(协)方差和连续样本路径(协)方差,并扩展HAR-RV-CJ模型,将(协)方差、共同跳跃置于统一波动模型框架内。通过对上证综指和深圳成指高频数据的实证分析,结果显示两指数共同跳跃占其各自的跳跃比例较大,且基本上都是同方向的跳跃;共同跳跃(协)方差和连续样本路径(协)方差对已实现(协)方差的影响都是显著的,考虑共同跳跃影响有助于提高(协)方差建模的准确性。此研究有助于投资者优化投资策略和为监管部门提供监管基础。
In consideration of the insufficience of the existing researches on co-jumps, co-jumps (co)variance and continuous sample path (co)variance are established using the common intraday jump test and the HAR-RV-CJ model is extended by taking (co)variance and co-jumps together into account, according to the existing theoretical framework. By virtue of high frequency data from Shanghai composite index and Shenzhen component index, the empirical analyses show that the number of the co-jumps of two indexes has a large proportion to their own jumps, most of the co-jumps are the same direction, co-jumps (co)variance and continuous sample path (co)variance both have significant effects on the (co)variance and considering co-jumps makes the extended model more accurate. This study makes contribution to the investment strategy optimization for investor and also provides regulatory basis for the regulatory authorities.
[1] 唐勇,张伯新.基于高频数据的中国股市跳跃特征实证分析[J].中国管理科学,2013,21(5):29-39.
[2] Barndorff-Nielsen O E, Shephard N. Measuring the impact of jumps in multivariate price processes using bipower covariation[R]. Working Paper,Nuffield College, Oxford University, 2004.
[3] Jacod J, Todorov V. Testing for common arrivals of jumps for discretely observed multidimensional processes[J]. The Annals of Statistics, 2009, 37(4): 1792-1838.
[4] Bollerslev T, Law T H, Tauchen G. Risk, jumps, and diversification[J]. Journal of Econometrics, 2008, 144(1): 234-256.
[5] Liao Yin, Anderson H M. Testing for co-jumps in high-frequency financial data: An approach based on first-high-low-last prices[R]. Working Paper Monash University, 2011.
[6] Gobbi F, Mancini C. Diffusion covartation and co-jumps in bidimensional asset price processes with stochastic volatility and infininte activityl levy jumps[R]. Working Paper, Universiy of Bologna,2008.
[7] Mancini C, Gobbi F. Identifying the Brownian covariation from the co-jumps given discrete observations[J]. Econometric Theory, 2012, 28(2): 249.
[8] Lahaye J, Laurent S, Neely C J. Jumps, cojumps and macro announcements[J]. Journal of Applied Econometrics, 2011, 26(6): 893-921.
[9] Dungey M, Hvozdyk L. Cojumping: Evidence from the US Treasury bond and futures markets[J]. Journal of Banking & Finance, 2012, 36(5): 1563-1575.
[10] Gilder D, Shackleton M B, Taylor S J. Cojumps in stock prices: Empirical evidence[J]. Journal of Banking & Finance, 2013,40(2):443-459.
[11] 欧丽莎,袁琛,李汉东.中国股票价格跳跃实证研究[J].管理科学学报,2011,14(9):60—66.
[12] Corsi F. A simple approximate long-memory model of realized volatility[J]. Journal of Financial Econometrics, 2009, 7(2): 174-196.
[13] Andersen T G, Bollerslev T, Diebold F X. Roughing it up: Including jump components in the measurement, modeling, and forecasting of return volatility[J]. The Review of Economics and Statistics, 2007, 89(4): 701-720.
[14] Corsi F, Renò R. Discrete-time volatility forecasting with persistent leverage effect and the link with continuous-time volatility modeling[J]. Journal of Business & Economic Statistics, 2012, 30(3): 368-380.
[15] Clements A, Liao Yin. The dynamics of co-jumps, volatility and correlation[R]. Working Paper,National Centre for Econometric Research, 2013.
[16] Andersen T G, Bollerslev T, Diebold F X, et al. Modeling and forecasting realized volatility [J]. Econometrica, 2003, 71(2): 579-625.
[17] Barndorff-Nielsen O E, Shephard N. Power and bipower variation with stochastic volatility and jumps [J]. Journal of financial econometrics, 2004, 2(1): 1-37.
[18] Bauwens L, Hafner C, Laurent B. Volatility models and their applications [M].New Jersy: Weily,2012.
[19] Andersen T G, Bollerslev T, Dobrev D. No-arbitrage semi-martingale restrictions for continuous-time volatility models subject to leverage effects, jumps and iid noise: Theory and testable distributional implications[J]. Journal of Econometrics, 2007, 138(1): 125-180.