基于非参数贝叶斯和因子降维方法的多元金融资产收益率和已实现协方差矩阵联合建模的研究

The ability to accurately characterize and forecast the conditional distribution of multivariate financial asset returns has always been key to multi-asset based financial decision-making, including the construction of optimal portfolios, etc. Meanwhile, with the expansion of the financial market, the number of assets involved in such decision-making is ever increasing. In addition to the emphasis on the goodness of fit and accuracy of forecast, multivariate return modeling also faces the challenge of handling high-dimensional data in real applications. Joint modeling of returns and realized covariance matrices(RCOV) has emerged as a new approach to modeling the return distribution. By using high-frequency data, this new approach has advantages over traditional low-frequency data based modeling methods, but there still exists great room for improvement. In this project we make a profound effort to extensively develop the joint modeling approach in various aspects, with the goal to address the current challenges from multivariate return modeling. We apply Bayesian nonparametric methods to the joint modeling of return and RCOV to build a brand new nonparametric model. It solves the problem of model misspecification and improves the theoretical characteristics of the model, resulting in improved fitting and forecasting ability. We also study how to employ factor-based dimension reduction method in the joint modeling to alleviate the “curse of dimensionality”. Finally, we combine our work of nonparameterization and dimension reduction innovation to the joint modeling to simultaneously cover the theoretical grounds and the need for high-dimensional applications, thus providing an effective solution to the accurate characterization of high-dimensional multivariate return distribution.

准确刻画和预测多元金融资产收益率的条件分布一直是包括构建最优资产组合在内的基于多资产的金融决策的关键。随着金融市场规模扩大，相关决策涉及的资产个数越来越多，当前对收益率模型的要求除了强调精确拟合和预测以外，同时越发兼顾模型处理高维数据的能力。新兴的对收益率和已实现协方差矩阵进行联合建模的方式利用高频数据刻画收益率分布，较传统基于低频数据的建模方式具有优势;但仍有局限。本项目针对当前收益率建模要求，对联合建模方法进行全面创新：一方面将非参数贝叶斯方法用于多元收益率和已实现协方差矩阵的联合建模，建立全新的非参化模型，从根本上解决模型误设问题，从而完善模型的理论特性并提高模型的拟合和预测能力；另一方面在联合建模中首次进行基于因子变换的降维方法的研究，以提高模型处理高维的能力；最后将联合建模的非参化和因子化进行有机的结合，兼顾模型的理论特性和高维应用，为高维收益率分布的准确刻画提供有效的解决方法。

本项目致力于多元金融资产收益率和以实现协方差矩阵（RCOV）贝叶斯非参化联合建模的研究。准确刻画和预测多元金融资产收益率的条件分布一直是包括构建最优资产组合在内的基于多资产的金融决策的关键。新兴的对收益率和RCOV联合建模的方式利用蕴藏丰富信息的日内高频数据刻画收益率分布，较传统基于低频数据的建模方式具有优势。随着金融市场规模扩大，相关决策涉及的资产个数越来越多，当前对收益率模型的要求除了强调精确拟合和预测以外，同时越发兼顾模型处理高维数据的能力。为了充分发挥联合建模方式用于刻画收益率分布的优势，满足当前对收益率条件分布建模的上述要求，本项目对现有联合建模方法进行了全面深入的创新研究，一方面致力于提高模型的拟合和预测的精度，另一方面力求提升模型处理高维数据的能力。.本项研究获得了以下重要成果：1. 利用威沙特和（逆）威沙特分布的共轭特性和线性变换下封闭的性质，建立了具有因子结构的收益率和RCOV的基于（逆）威沙特—多元正太分布的参数化联合模型，提高了参数模型处理高维数据的能力；2. 采用基于贝叶斯DPM和HDP非参先验的无限混合（逆）威沙特—多元正太分布构造收益率和RCOV联合模型，从根本上解决参数化建模的误设问题，实现了多元收益率分布的精准刻画，从而提高模型的拟合和预测能力；3. 在收益率和RCOV的贝叶斯非参数化联合模型中成功植入了因子结构，建立起全新的具有降维机制的非参化联合模型，兼顾了理论特性和高维应用，从而有效解决高维收益率分布的精准刻画和预测问题。