异质金融市场驱动的高维高频波动率矩阵模型及其应用研究

High-dimensional volatility matrix is the basic and kernel element for importent financial theories and activities concluding high-dimensional asset allocation、asset pricing and risk management. Its estimation and modelling is always the focus in reletive research. The project is to thoroughly and systematically research on high-dimensional and high-frequency volatility matrix models driven by heterogeneous market. Models the project proposed are flexible and easy realized; can use abundant direct information about volatility; by combining with heterogeneous market hypothesis, can deal with two problems faced by traditional low-frequency models , i.e. lackness of economical interpretations and dimension curse; provide probability to explore the microstructural fator in price fluctuation. The content of this project is divided into three parts. The first one is to propose blocking synchronization approach, and based on it, develop methodologies for estimating high-dimensional and high-frequency volatility matrix. The second one is to construct a system of heterogeneous market-driven factors, develop the factor analyses for volatility matrix, and build high-dimensional and high-frequency volatility matrix models. The last is to build the bootstrap estimator and hypothesis testing model for VaR and CVaR of high dimentional Portfolio based on united mean-volatility model of high dimentional return ratio. The research achievements of the project will establish a complete system of basic theories and applications of high-dimensional and high-frequency volatility matrix models.

高维波动率矩阵是高维资产配置、资产定价及风险管理等重要金融理论和活动的基础与核心要素，其估计与建模一直是相关研究的重点。本项目对异质市场驱动的高维高频波动率模型及其应用展开深入系统研究。提出具有建模灵活且易于实现、可利用直接丰富波动信息等优势的高维高频波动率矩阵模型，其与异质市场假说的结合，解决传统低频模型存在的经济解释欠缺性和维数灾难两大问题，并为探寻价格波动的微观结构因素提供可能。研究内容分为：（1）非同步和微观结构噪声下，分块式同步化技术，及在此基础上高维高频波动率矩阵估计问题研究；（2）构建高维高频波动率矩阵的异质市场驱动因素体系，完善和发展波动率矩阵因子分析技术，建立高维高频波动率模型；（3）基于高维收益率均值-波动率联合模型，建立高维资产组合VaR和CVaR 的Bootstrap估计与检验模型。项目研究成果将形成一个完整的高维高频波动率矩阵模型基础理论和应用体系。

本研究对异质市场驱动的高维高频波动率模型及其应用展开了深入系统的研究，得到如下研究结果：（1）借助聚类分析手段，完善了已有分块式同步化技术，并提出新的适用于高频极差分析的同步化技术；（2）借助资产间协方差公式的分解，提出了基于极差的协方差阵估计技术及其相应的纠偏技术；该技术可更有效地利用日内丰富的波动信息；（3）通过在现有的CAW模型中引入我们构建的三级异质市场驱动因素体系，形成新的HAR-CAW-L-M模型。该波动率矩阵模型具有较好的经济意义，其直接基于波动率矩阵的建模可一定程度上缓解“维数危机”问题。其进一步与矩阵型因子分析的结合，可起到矩阵降维作用。（4）编写了一整套相关模型的计算实现程序，并据此展开了协方差矩阵估计技术的数值模型研究，结果发现与现有基于收益的估计相比，我们所提估计的偏差、均方误差等指标表现更优；（5）展开了各模型在组合资产配置、套期保值、波动溢出等金融问题中的应用研究及其实证分析，研究结果表明我们所提模型要优于各传统模型。