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。