噪声方差、跳跃波动、连续波动的分离及其相互关系——来自中国股市的实证研究

Separating noise variance from jump volatility and continuous volatility and the relationships among them:Evidence from the Chinese stock market

本文在市场微观结构噪声和跳跃下将Jing等[1]中的预平均门限已实现方差这一连续波动估计拓展到允许噪声过程的条件方差为时变的情形。我们分别采用预平均和门限的方法消除噪声和跳跃的影响,同时给出其渐近性质。蒙特卡罗模拟结果表明这一估计对噪声和Lévy跳跃稳健并且相比同类连续波动估计具有更好的表现。鉴于这一估计的优良性质,本文还通过蒙特卡罗模拟探讨门限和预平均水平的选取以及移动平均噪声,舍入噪声和相依结构噪声等时变条件方差噪声对该估计的影响。在实证分析中,本文首先基于这一改进的估计从2014到2015年上证50成分股Level-2的逐笔交易数据中分离出噪声方差、跳跃波动和连续波动。然后,采用面板向量自回归模型研究三者之间相互关系,发现噪声方差与连续波动之间存在显著正的双向Granger因果关系;连续波动和噪声方差均是跳跃波动的Granger原因,但是反过来不成立。最后,利用拓展的异质自回归(HAR)模型来研究噪声方差对连续波动和跳跃波动的预测能力,发现噪声方差对有效价格的波动具有正向预测作用,该预测作用不仅针对连续波动,而且对跳跃波动具有显著预测能力,但前者显著性更强。

Volatility modeling is one of the core topics in finance and financial econometrics.It has wide applications in risk management,asset pricing,and asset allocation.In recent years,extreme volatilities occurred in the Chinese financial market from time to time.For example,during 2014-2015,the Chinese stock market underwent extreme market conditions:the stock market sharp rally was followed by a sharp plunged,which eventually evolved into a crash.In particular,the abnormal volatilities from June to August in 2015 caused investors and regulators to concern about financial risks.Existing volatility modeling methodologies are largely based on low-frequency data.The most widely used models include GARCH and stochastic volatility(SV)models.Although these models can capture the main characteristics of financial market volatility,they are subject to a few limitations.First,these models are parametric in spirit and thus may suffer from model misspecification.Second,these models only use low frequency returns to estimate and forecast volatility without considering intraday sample information.The estimates may be biased,leading to nontrivial forecast errors.Last,the parametric estimation procedure for these models remains very complicated,especially for the SV model.In the multivariate case,these models are constantly challenged by the curse of dimensionality,and therefore are of limited use in real applications.Recently,with easier access to high-frequency data and the rise of high frequency trading,an increasing number of studies begin to use high-frequency data to estimate,model and predict volatility.One of the most famous proxy variables for volatility is so-called realized volatility(RV).RV has several merits:it is nonparametric and thus requires less assumptions on model set-up.As a matter of fact,it only imposes the assumption of no arbitrage opportunities.Besides,RV is a direct proxy for volatility,it is not necessary to obtain the embedded volatility like the GARCH model.Last but not least,many studies find the forecasting performance of the simple time series model for RV can beat the GARCH model.However,there are several challenges when using high frequency data to estimate volatility.First,many studies show that jump should be included in asset prices.In the presence of jumps,RV is indeed an estimation of the sum of continuous volatility(CV)and jump volatility(JV).Since CV and JV represent different types of risk,it is necessary to disentangle them from each other in real applications.Two most famous estimations for CV are the multipower estimation and truncated realized variance estimation.Second,the observed high-frequency prices are usually contaminated by noise due to but not limited to bid-ask spread,information asymmetry,discreetness of price,etc.Under these scenarios,RV is no longer a consistent estimation of CV,and the size of bias determinates as the sampling frequency increases.There are several ways to alleviate the effects of noise when estimating CV.One common strategy is using the subsampling method,which,however,will lead to information loss.Other methodologies include the two-scale realized variance(TSRV)or multiscale realized variance(MSRV)estimation,the realized kernel estimation,the pre-averaging method,the quasi maximum likelihood estimation(QMLE),and the local moment estimation(LMM),etc.But most of them assume that noise process is independent of the underlying asset price and serially independent.For example,the TSRV(MSRV)and QMLE estimation assume that noise is i.i.d.,while the pre-averaging method assumes that noise is conditionally independent.However,empirical studies reveal that noise is time varying,dependent and correlated with the underlying asset price.These stylized facts are much more complicated than the assumptions underlie the models.Therefore,it is important to improve the accuracy of volatility measurement,as well as to separate noise variance,CV and JV from noisy high frequency data.By doing so,we can improve the management of volatility and market risk surveillance.In view of these facts,this paper extends the pre-averaged threshold realized variance estimator for integrated volatility in Jing,et al[1]to the case with time-varying conditional variance of market microstructure noise and jumps.By using pre-averaging and threshold technique,we can remove the microstructure noise and jumps,respectively.The asymptotic properties of this new estimator,including the consistency and associated central limit theorems,are also provided.Monte Carlo simulations show that the estimator is robust to both microstructure noise and Lévy jumps,and it provides less biased estimation,compared with existing estimators,of continuous variations in finite samples.We also illustrate,through Monte Carlo simulations,how the choice of threshold and preaveraging parameters,as well as noise with time-varying conditional variance(e.g.the moving average noise,rounding noise and dependent noise)affect the CV estimation.In the empirical analysis part,we use the improved pre-averaged threshold realized variance estimation on the Level-2 high frequency data for SSE 50 component stocks from 2014 to 2015.We separate noise variance,jump volatility and continuous volatility and study the relationships among these volatilities using panel vector autoregressive models.Then,we investigate the predictive power of noise variance on CV and JV using the extended HAR models.The main findings are summarized as follows.There exists bidirectional Granger causality between noise variance and CV.Both CV and noise variance Grangercause JV,but not vice versa.Noise variance has positive predictive power for underlying return volatility,and such predictability holds for both CV and JV,especially for the former.