基于高频数据的金融资产价格过程模型设定检验与协同波动率估计

A large number of empirical studies based on financial high frequency data show that financial asset returns have the property of long memory. However, most of the existing research of the financial asset price process in high frequency environment considers jumps and microstructure noise components. Moreover, the type of microstructure noise is not detected at the same time. This project will unify three random components, including long memory, jump and microstructure noise, into one theoretical model, and use nonparametric methods to test financial asset price model specification and estimate co-volatility. First, we use two step variance and Bayesian methods to test single asset price process model specification, and construct the related statistics to test long memory component and microstructure noise component, and identify the types of the microstructure noise. Second, the time varying power variation and random matrix technique are used to test the co-jump phenomena and the time-varying correlations among multiple assets. Then, based on the combination of the quasi maximum likelihood method and the threshold power variation technique, we study the estimation problem of the co-volatility. Finally, we use the high frequency data of China's financial market to carry on the empirical research, in order to get the proper financial asset price models and more precise volatility estimators. The research results not only improve the modeling theory of financial high frequency data, but also enrich the risk management theory, which has positive guiding significance for portfolio optimization and asset pricing in reality.

大量金融高频数据的实证研究发现资产收益率具有长记忆性，而目前已有高频环境下金融资产价格变化过程大多只考虑跳跃与微结构噪音成分，而且未甄别微结构噪音的类型。本项目将长记忆性、随机跳跃和微结构噪音三种随机成分纳入同一个理论模型，采用非参数方法研究金融资产价格模型的设定检验问题和协同波动率的估计问题。首先，采用两阶段方差和贝叶斯方法研究单个资产价格模型的设定检验问题，构造检验长记忆性成分和微结构噪音成分的统计量，并辨别微结构噪音的类型。其次，采用时变幂变差和随机矩阵技术研究多个资产之间的共同跳跃现象与时变相关关系。然后，结合拟极大似然法与门限幂变差技术研究协同波动率的估计问题。最后，采用我国金融市场的高频数据对项目所得统计量进行实证研究，以期得到适合我国实际的金融资产价格模型与波动率估计量。研究结果不仅完善了金融高频数据建模理论，也丰富了风险管理理论，对投资组合和资产定价具有积极指导意义。

大量金融高频数据的实证研究发现资产收益率具有长记忆性，而目前已有高频环境下金融资产价格变化过程大多只考虑跳跃与微结构噪音成分，对微结构噪音的类型未进行甄别。本项目将长记忆性、随机跳跃和微结构噪音三种随机成分纳入同一个理论模型，采用多种参数估计方法研究金融资产价格模型的设定检验问题和协同波动率的估计问题。首先，在连续观察的情况下，我们采用最小二乘方法研究了分数Vasicek模型下的参数估计问题，并对金融波动率的泡沫模型进行了分析。其次，在金融标的资产服从几何分数高斯过程框架下，采用随机分析方法，利用无套利金融市场理论，我们构建了一般分数高斯环境下金融市场的套利策略。最后，将跳跃效应纳入公司价值动态变化过程，并在企业的杠杆作用框架下，研究了包含债务的股权权证定价问题，构建股本权证的定价模型。研究结果不仅完善了金融高频数据建模理论，也丰富了风险管理和资产定价理论，对投资组合也具有积极指导意义。