混合正态双因子已实现SV模型及其实证研究

Two-factor Realized SV Model with Mixture of Normals and Its Empirical Research

传统的波动率模型(如GARCH模型和SV模型)采用日度收益率数据对波动率建模,忽略了日内高频数据包含的丰富信息。同时,资产收益率的波动率往往展现长记忆性,资产收益率的分布展现非正态性(尖峰、厚尾),传统的波动率模型不能很好地刻画现实资产收益率的这些特征。将包含丰富日内高频信息的已实现波动率引入传统低频SV模型中,同时考虑已实现波动率偏差修正、波动率长记忆性和资产收益率的非正态性(尖峰、厚尾),构建混合正态双因子已实现SV(2FRSV-MN)模型。为了估计2FRSV-MN模型的参数,给出灵活且易于实现的基于连续粒子滤波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分指数5分钟高频交易数据,对提出的2FRSV-MN模型进行实证检验。研究结果表明,已实现波动率是真实日度波动率的有偏估计(下偏),沪深股市非交易时间效应强于微观结构噪声效应;沪深股市具有强的波动率持续性和显著的杠杆效应,且杠杆效应只存在于短记忆波动率因子过程中,长记忆波动率因子过程中存在反向杠杆效应;根据赤池信息准则,2FRSV-MN模型比其他模型具有更好的数据拟合效果。对风险值的估计结果表明,2FRSV-MN模型能较好地测量金融市场风险,但并非一定是具有最好的风险测量效果的模型,这取决于选取的概率和数据。研究结果不仅为投资者和监管机构提供了信息和决策参考,也丰富了基于高频数据的波动率建模和市场风险测量的研究。

The traditional volatility models,such as the GARCH model and SV model,use only daily returns data to model volatility. However,they do not take advantage of additional information provided by high-frequency intra-day data. In addition,it has been well documented that the volatility of asset returns exhibits the property of long-range dependence and the empirical distribution of asset returns exhibits non-normality( leptokurtosis and heavy-tails). The traditional volatility models fail to account for these empirical stylized facts of realistic asset returns.This paper incorporates the low-frequency SV model with high-frequency intra-day information provided by the realized volatility( RV) and proposes the two-factor realized SV model with mixture of normals( 2 FRSV-MN model). The model takes the RV biases,long memory property of the volatility and non-normality of the asset returns into consideration. To estimate the parameters of the model,the maximum likelihood estimation method based on the continuous particle filters is developed. Monte Carlo simulation study shows that the estimation method performs well. We apply the 2 FRSV-MN model to the 5-min high-frequency intra-day data of Shanghai Stock Exchange composite( SSE) index and Shenzhen Stock Exchange component( SZSE) index.The results show that the RV is a( downward) biased estimator of the true daily volatility. This implies that the effect of non-trading hours is stronger than that of microstructure noise. Evidence of strong volatility persistence and significant leverage effect is detected in Shanghai and Shenzhen stock markets. Moreover,we do find the strong evidence of leverage effect in the short-memory volatility process,while reverse leverage effect is found in the long-memory volatility process. According to the Akaike information criterion( AIC),the 2 FRSV-MN model fits the data better than the others. The empirical findings,based on the Value at Risk( VaR) estimates,indicate that the 2 FRSV-MN model performs well. However,the 2 FRSV-MN model is not necessary to be the best model,and the risk measurement performance of the model is sensitive to the choice of the probability and data.This paper not only provides some information and decision-making reference for the investors and regulators,but also enriches the empirical research on the volatility modelling and market risk measurement based on the high-frequency data.