在基本的SV模型中引入包含丰富日内高频信息的已实现测度，同时考虑其偏差修正以及波动率非对称性与长记忆性，构建了双因子非对称已实现SV（2FARSV）模型.进一步基于连续粒子滤波算法，给出了2FARSV模型参数的极大似然估计方法.蒙特卡罗模拟实验表明，给出的估计方法是有效的.采用上证综合指数和深证成份指数日内高频数据计算已实现波动率（RV）和已实现极差波动率（RRV），对2FARSV模型进行了实证研究.结果表明：RV和RRV都是真实日度波动率的有偏估计（下偏），但RRV相比RV是更有效的波动率估计量；沪深股市具有强的波动率持续性以及显著的波动率非对称性（杠杆效应与规模效应）；2FARSV模型相比其它已实现波动率模型具有更好的数据拟合效果，该模型能够充分地捕获沪深股市波动率的动态特征（时变性、聚集性、非对称性与长记忆性）.
Modelling the volatility has attracted a great deal of attention in the literature of financial economics and econometrics. As a measure of risk, volatility modelling is important to researchers, policy makers and regulators as it is closely related to the stability of financial markets, and the SV models are used to model the dynamics of volatility. It has been well-documented in the literature that the volatility exhibits two typical features, namely the asymmetric effects (include leverage and size effects) on volatility caused by previous returns and the long-range dependence in volatility. It is important to accommodate these features in volatility in the SV models.
In recent years, high-frequency financial data is available and a number of realized measures of volatility have been introduced, including realized volatility and realized range volatility. These measures are far more informative about the current level of volatility than the daily returns. Standard SV models utilizes daily returns to extract information about the current level of volatility. A shortcoming of conventional SV models is the fact that returns are rather weak signals about the level of volatility. This makes SV models poorly suited for situations where volatility changes rapidly to a new level. Incorporating realized measures into SV models is expected to alleviate this problem.
Based on the above analysis, in this paper the two-factor asymmetric realized SV (2FARSV) model is proposed, which incorporates the basic SV model (which uses daily returns) with asymmetric effects (leverage and size effects), long memory property of the volatility and high-frequency intraday information provided by the realized measure by taking account of the realized measure biases. A maximum likelihood estimation method based on the continuous particle filters is used to estimate the parameters of the 2FARSV model. The monte Carlo simulation study shows that the estimation method performs well. The 2FARSV model is appiled to the realized volatility (RV) and realized range volatility (RRV) computed from the high-frequency intraday data of Shanghai Stock Exchange composite index and Shenzhen Stock Exchange component index. The results show that the RV and RRV are (downward) biased estimators of the true daily volatility. This implies that the effect of non-trading hours is stronger than that of microstructure noise. The RRV is the more effective volatility estimator than the RV, but it leads to more downward bias. In addition, evidence of strong volatility persistence and volatility asymmetry (leverage and size effects) is detected in Shanghai and Shenzhen stock markets. According to the Akaike information criterion (AIC) and Bayesian information criterion (BIC), the 2FARSV model fits the data better than the one-factor asymmetric realized SV (1FARSV) model, the two-factor realized SV (2FRSV) model, the two-factor leverage realized SV (2FLRSV) model and the realized GARCH model. Model diagnostics suggest that the 2FARSV model is sufficient to capture the dynamics of the volatility (time-varying volatility, volatility clustering, volatility asymmetry and long memory property of the volatility).
This study enriches the empirical research on the volatility modelling based on the high-frequency data.It's also a worthwhile endeavor to further investigate the performance of the 2FARSV model in asset pricing and value-at-risk calculation.
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