考虑跳跃和隔夜波动的中国股票市场波动率建模与预测

摘要/Abstract

摘要： 本文用已实现波动率（Realized Volatility， RV）度量上证综指和深证成指在交易时间内的波动率，并将其分解为连续路径变差部分和由跳跃引起的非连续部分。这两部分与隔夜波动率共同构成日波动率。本文对日波动率的三个组成部分建立HAR-CJN模型，探究了波动率不同成分之间的相互影响以及在预测中的作用。结果表明连续变差对日波动率的各组成部分均有显著的正向影响，在预测中的贡献最大；而跳变差的影响一般比连续变差的要弱，且随着滞后期的长短而有所不同。样本外预测结果显示HAR-CJN模型的预测表现要远远优于GARCH族模型，并在向前一天和一月的预测中优于普通的HAR-RV模型。

关键词: 已实现波动率, 跳跃, 隔夜波动率, 预测

Abstract: Daily volatility of Shanghai Stock Exchange Composite Index and Shenzhen Stock Exchange Component Index are decomposed into three components, which are the continuous sample-path variation, the discontinuous variation due to jumps and the overnight variance. Then HAR-CJN model is proposed to study the interaction of the three components and their impact on forecasting. The results show that the continuous variation has positive impact on each of the three components and contributes the most in forecasting, while the impact from jump variation is generally weaker than that from continuous variation and varies in direction and size as the length of lag-period changes. The out-of-sample forecast results show that HAR-CJN model outperforms traditional GARCH model considerably, and also outperforms the popular realized volatility model HAR-RV in the one-day-ahead and one-month ahead forecast.

Key words: realized volatility, jump, overnight variance, forecast

中图分类号:

F830

孙洁. 考虑跳跃和隔夜波动的中国股票市场波动率建模与预测[J]. 中国管理科学, 2014, 22(6): 114-124.

SUN Jie. Modeling and Forecasting the Volatility of China Stock Market Considering the Impact of Jump and Overnight Variance[J]. Chinese Journal of Management Science, 2014, 22(6): 114-124.

参考文献

[1] Andersen T G, Bollerslev T. Answering the skeptics: Yes, standard volatility models do provide accurate forecasts[J]. International Economic Review, 1998, 39(4): 885-905.

[2] Andersen T G, Bollerslev T, Diebold F X, et al. Modeling and forecasting realized volatility[J]. Econometrica,2003, 71(2): 579-625.

[3] Corsi F. A simple approximate long-memory model of realized volatility[J]. Journal of Financial Econometrics, 2009, 7 (2): 174-196.

[4] Merton R C. Option pricing when underlying stock returns are discontinuous[J]. Journal of Financial Economics, 1976, 3(1–2): 125-144.

[5] 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.

[6] Barndorff-Nielsen O E, Shephard N. Econometrics of testing for jumps in financial economics using bipower variation[J]. Journal of Financial Econometrics, 2006, 4 (1): 1-30.

[7] Todorov V, Bollerslev T. Jumps and betas: A new framework for disentangling and estimating systematic risks[J]. Journal of Econometrics,2010, 157(2): 220-235.

[8] 陈浪南,孙坚强. 股票市场资产收益的跳跃行为研究[J]. 经济研究, 2010,(4): 54-66.

[9] 沈根祥. 沪深300指数跳的逐点检验及动态分析[J]. 中国管理科学, 2012,(1): 43-50.

[10] Andersen T G, Bollerslev T, Diebold F X. Roughing it up: including jump components in the measurement, modeling, and forecasting of return volatility[J]. Review of Economics and Statistics, 2007, 89(4): 701-720.

[11] Bollerslev T, Tauchen G, Zhou Hao. Expected Stock Returns and Variance Risk Premia[J]. Review of Financial Studies. 2009, 22 (11): 4463-4492.

[12] Andersen T G, Bollerslev T, Huang X. A reduced form framework for modeling volatility of speculative prices based on realized variation measures[J]. Journal of Econometrics, 2011, 160(1): 176-189.

[13] Corsi F, Reno 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.

[14] 徐正国,张世英. 调整"已实现"波动率与GARCH及SV模型对波动的预测能力的比较研究[J]. 系统工程,2004,22(8):60-63.

[15] 魏宇,余怒涛. 中国股票市场的波动率预测模型及其SPA检验[J]. 金融研究, 2007,(07):138-150.

[16] 魏宇. 沪深300股指期货的波动率预测模型研究[J]. 管理科学学报, 2010,(2): 66-76.

[17] 张小斐,田金方. 异质金融市场驱动的已实现波动率计量模型[J]. 数量经济技术经济研究, 2011,(9): 140-153.

[18] 王春峰,姚宁,房振明,等. 中国股市已实现波动率的跳跃行为研究[J]. 系统工程, 2008,(2): 1-6.

[19] 魏宇. 沪深300股指期货的波动率预测模型研究[J]. 管理科学学报, 2010,13(2):66-76.

[20] Engle R F, Russell J R. Autoregressive conditional duration: A new model for irregularly spaced transaction data[J]. Econometrica, 1998, 66(5): 1127-1162.

[21] Lee S S, Mykland P A. Jumps in financial markets: A new nonparametric test and jump dynamics[J]. Review of Financial studies, 2008, 21(6): 2535-2563.

[22] Koopman S J, Jungbacker B, Hol E. Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements[J]. Journal of Empirical Finance, 2005, 12(3): 445-475.

[23] Hansen P R, Lunde A. Realized variance and market microstructure noise[J]. Journal of Business and Economic Statistics, 2006, 24(2): 127-161.

[24] Diebold F X, Mariano R S. Comparing predictive accuracy[J]. Journal of Business & Economic Statistics, 2002, 20(1): 134-144.

[25] 王天一,黄卓. 高频数据波动率建模——基于厚尾分布的Realized GARCH模型[J]. 数量经济技术经济研究, 2012,(5): 149-161.

[26] Mincer J A, Zarnowitz V. The evaluation of economic forecasts.Working Paper, NBER, 1969.