基于高维高频金融数据的最小方差组合风险的估计及应用  

Estimation and Application of Minimum Variance Portfolio Risk Based on High Dimensional and High Frequency Financial Data

作　　者：刘丽萍[1] 吕政 LIU Liping;Lü Zheng(School of Mathematics and Statistics,Guizhou University of Finance and Economics,Guiyang 550025;School of Statistics and Mathematics,Central University of Finance and Economics,Beijing 102206)

机构地区：[1]贵州财经大学数学与统计学院,贵阳550025 [2]中央财经大学统计与数学学院,北京102206

出　　处：《系统科学与数学》2021年第10期2948-2964,共17页Journal of Systems Science and Mathematical Sciences

基　　金：贵州省科技厅一般项目(黔科合基础[2019]1050);贵州省教育厅科技人才成长项目(黔教合KY字[2018]160);2018贵州财经大学校级项目(2018XYB10);2020年贵州财经大学校级项目(2020XYB06)资助课题。

摘　　要：对于高维高频的金融大数据,噪声、跳跃以及非同步交易的影响,使得在投资组合中扮演着重要角色的协方差阵的估计更为复杂.文章首先回顾了考虑噪声、跳跃影响的高频协方差阵估计量,并对非同步交易所导致的数据损失情况进行了分析.然后为减少数据的损失,提出了基于分块策略和正则化方法的高频协方差阵估计量.最后构造了基CLIME(the constrained L1 minimization for inverse matrix estimation)估计量的最小方差投资组合模型,并将文章所构造的协方差阵估计量代入其中,得到基于高维高频数据的最小方差组合风险的估计形式.通过模拟和实证研究发现:同时考虑了噪声、跳跃以及非同步交易影响的高频协方差阵,其所构造的CLIME估计量的组合风险与真实的风险最为接近.For high-dimensional and high-frequency financial big data,the estimation of covariance matrix,which plays an important role in portfolio,is more complex due to the influence of noise,jump and asynchronous trading.In this paper,we first review the high-frequency covariance matrix estimators which considering the effects of noise and jump,and analyze the data loss caused by asynchronous exchanges.Then,in order to reduce the data loss,a high frequency covariance matrix estimator based on blocking strategy and regularization method is proposed.Finally,the minimum variance portfolio model based on CLIME(the constrained L1 minimization for inverse matrix estimation) estimator is constructed,and the covariance matrix estimator constructed in this paper is substituted into it to statistically estimate the risk of the minimum variance portfolio of high-dimensional and high-frequency financial big data.Through simulation and empirical study,it is found that the combined risk of the CLIME estimator based on high-frequency covariance matrix that takes into account the effects of noise,jump,and asynchronous trading is closest to the real risk.

关 键 词：金融大数据 最小方差投资组合 CLIME估计量 分块策略 

分 类 号：F832.51[经济管理—金融学] F224