Abstract: The modelling and forecasting of asset volatility are critical for financial risk management and derivatives pricing. Instead of treating volatility as an unobservable variable, recent works in this area tend to construct the Realized Volatility (RV) estimator proposed by ANDERSEN and BOLLERSLEV (1998) using high-frequency intraday prices and then model the observable RV estimator directly, most of which apply the Heterogeneous Autoregressive (HAR) model proposed by CORSI (2009) and its various extensions.
   To improve the prediction ability of the HAR class models, some researchers further decomposed the realized volatility. Among them, ANDERSEN et al. (2007) decomposed the realized volatility into the continuous component (C) and the jump component (J), constructed the HAR-RV-CJ model which separated the contribution of continuous and jump components and achieved better forecasting performance. PATTON and SHEPPARD (2015) decomposed the realized volatility into the Realized Positive and Negative Semivariances (RS) based on the sign of intraday returns, constructed the HAR-RV-RS model which characterized the intraday leverage effect and achieved better forecasting performance as well.
   Considering that intraday returns of different levels can have different amount of valuable information for future volatility, this study decomposes the realized volatility into the high-return variation, the medium-return variation and the low-return variation based on the level of intraday returns, and constructs the HAR-RV-R model that separates the contribution of these three variations following the HAR-RV-RS model of PATTON and SHEPPARD (2015).
   The empirical experiments using intraday five-minute prices of the Shanghai Stock Exchange index show that the HAR-RV-R model has a better in-sample fit and out-of-sample forecasting performance than the benchmark HAR-RV-RS model, which proves that the realized volatility decomposition based on the level of intraday returns is more effective than the decomposition based on the sign of intraday returns. Furthermore, such a superiority of the proposed HAR-RV-R model is consistent as the prediction horizon increases from one day to one week and then one month, and the superiority of the HAR-RV-R model is statistically significant, as justified by the Diebold-Mariano test. Further examination of the explanatory power of the high-return variation, the medium-return variation and the low-return variation on future volatility shows that the medium-return variation has outstanding explanatory power compared with the high-return variation and the low-return variation.
   In order to compare the explanatory power of the high-return variation, the medium-return variation and the low-return variation of different time horizons, we extend the HAR-RV-R model to the HAR-RV-RHML model, which includes the daily, the weekly and the monthly high-return variations, medium-return variations and low-return variations as regressors. The empirical results show that the HAR-RV-RHML model has a significantly better out-of-sample prediction performance than the HAR-RV-R model for all the three forecast horizons, and the explanatory power of the daily, the weekly and the monthly variations is clearly different, with the monthly variables having the strongest explanatory power.
   Finally, considering that the medium-return variation is essentially a removement of the jump component of the realized volatility, this study compares the explanatory power of the medium-return variation with that of various continuous volatility estimators constructed with major jump identification methods. The empirical evidence points out that the model introducing the medium-return variation has a stronger out-of-sample forecasting performance, which confirms that the realized volatility decomposition based on the level of intraday returns is simple but effective.
   The proposed realized volatility decomposition method and the corresponding empirical results are valuable for practical applications such as financial risk management and derivatives pricing. Further extensions include the appropriate decomposition of the realized covariance matrix so as to improve the prediction ability, which can contribute to the practical application of asset allocation.

Key words: volatility forecast, realized volatility, HAR model, intraday return level, volatility decomposition, jump

摘要： 考虑到不同水平的日内收益可能蕴含不同的市场未来波动有益信息,基于日内收益水平将已实现波动分解为高、中、低收益变差,并参考PATTON和SHEPPARD(2015)的HAR-RV-RS模型构建区分高、中、低收益变差贡献的HAR-RV-R模型。采用中国股票指数五分钟数据的实证表明,HAR-RV-R模型相比HAR-RV-RS模型在拟合与预测上都有明显改进,证明基于日内收益水平的已实现波动分解更为有效。进一步地,分别考察高、中、低收益变差对指数未来波动的解释能力,实证表明:(1)相对于高、低收益变差,中收益变差具有突出的解释能力;(2)高、中、低收益变差的日、周、月变量解释能力有明显分化,且月变量解释能力最强。最后,考虑到中收益变差本质上也是对波动中跳跃成分的一种剥离,对比其与多种跳跃识别方法下构建的连续波动估计量对未来波动的解释能力,实证指出引入中收益变差的模型具有更强的样本外预测精度,再次说明基于日内收益水平的已实现波动分解虽简单但有效。本文提出的已实现波动分解方法及实证结论对于风险管理与衍生产品定价等金融实务都具有重要价值。

关键词: 波动率预测, 已实现波动率, HAR模型, 日内收益水平, 波动率分解, 跳跃