Large volatility matrix estimation with factor-based diffusion model for high-frequency financial data

Abstract

Large volatility matrices are involved in many finance practices, and estimating large volatility matrices based on high-frequency financial data encounters the “curse of dimensionality”. It is a common approach to impose a sparsity assumption on the large volatility matrices to produce consistent volatility matrix estimators. However, due to the existence of common factors, assets are highly correlated with each other, and it is not reasonable to assume the volatility matrices are sparse in financial applications. This paper incorporates factor influence in the asset pricing model and investigates large volatility matrix estimation under the factor price model together with some sparsity assumption. We propose to model asset prices by assuming that asset prices are governed by common factors and that the assets with similar characteristics share the same association with the factors. We then impose some reasonable sparsity condition on the part of the volatility matrices after accounting for the factor contribution. Under the proposed factor-based model and sparsity assumption, we develop an estimation scheme called “blocking and regularizing”. Asymptotic properties of the proposed estimator are studied, and its finite sample performance is tested via extensive numerical studies to support theoretical results.