信息不对称下成交量与波动率关系建模与统计推断  

The Modelling and Statistical Inference of Volume-Volatility Relation under Information Asymmetry

作　　者：彭烨 张志远 Peng Ye;Zhang Zhiyuan

机构地区：[1]上海财经大学 [2]上海财经大学统计与管理学院

出　　处：《统计研究》2023年第3期100-113,共14页Statistical Research

基　　金：国家自然科学基金面上项目“金融高频大数据下的风险推断及其与多元标的衍生品定价和金融风险管理的交叉融合研究”(71871132);国家自然科学基金委重大研究计划重点项目“金融大数据统计推断理论与方法及应用研究”(91546202);中央高校基本科研业务费(批准号:CXJJ-2019-412)专项资金资助;部分受到上海市数据科技与决策前沿科学研究基地(Shanghai Research Center for Data Science and Decision Technology)资助。

摘　　要：本文首次提出信息不对称背景下成交量和波动率关系的日度完备模型。新模型假设当日成交量和已实现测度为次日隐信息流带来新信息,而隐信息流驱动知情交易者交易。基于此模型,本文给出时间序列平稳遍历性成立的充分条件,并且运用高斯拟极大似然法,建立模型参数估计的渐近理论,模拟研究验证了渐近理论的正确性。本文将新模型应用于中国沪深A股市场、美国纽交所和纳斯达克市场的大型公司。基于全样本的模型拟合结果发现:成交量的放大将导致次日条件波动率增大,而条件波动率的增大伴随着成交量的放大,同时,大部分个股中存在信息交易;在存续时间长、市值靠前且交易活跃的中国个股中,相较于基准波动率模型——已实现GARCH模型,新模型大多具有更好的样本内拟合能力;而在市值靠前且交易活跃的美股中,新模型的表现并不优于已实现GARCH模型。在滚动窗口的波动率预测上,较其他被广泛使用的已有模型,新模型在本文研究的中国个股中普遍具有更好的表现;而在本文研究的美股中,已实现GARCH模型表现较好。这反映了新模型更加适用于存续时间长、市值靠前且交易活跃的中国股票市场数据。We propose a realized Mixture of Distribution Hypothesis model for volume-volatility relation under information asymmetry.The model hypothesizes that the trading volume of the day and the realized measurement provides new information for the second-day potential information flow,which drives informed trading.Sufficient conditions for the stationarity and ergodicity of the time series under our modelling framework are provided.A Gaussian quasi-maximum likelihood estimation method for parameter estimation is proposed and its asymptotic theory is established.Simulation results corroborate our theoretical findings.The proposed model and method are applied to both the U.S.and China stock data.Empirical results show that the increase of trading volume will lead to the increase of the second-day conditional volatility,and that our model fits the data of large-cap,long listed and highly liquid stocks from the Chinese market better than the realized GARCH model as the benchmark volatility model.We find that information trading exists in most stocks.Moreover,our model outperforms widely used existing models in volatility forecasting when applied to Chinese stocks,while the realized GARCH model performs better in U.S.stocks.In summary,our model is more appropriate for describing data of large-cap,long listed and highly liquid stocks from the Chinese market than existing models.

关 键 词：混合分布假说 成交量与波动率关系 已实现GARCH 拟极大似然估计 平稳遍历性 

分 类 号：O212[理学—概率论与数理统计]