Factor GARCH-ITO Models for High-Frequency Data with Application to Large Volatility Matrix Prediction

41 Pages Posted: 13 Dec 2017

See all articles by Donggyu Kim

Donggyu Kim

KAIST College of Business

Jianqing Fan

Princeton University - Bendheim Center for Finance

Date Written: December 8, 2017

Abstract

Several novel large volatility matrix estimation methods have been developed based on the high-frequency financial data. They often employ the approximate factor model that leads to a low-rank plus sparse structure for the integrated volatility matrix and facilitates estimation of large volatility matrices. However, for predicting future volatility matrices, these nonparametric estimators do not have a dynamic structure to implement. In this paper, we introduce a novel Ito diffusion process based on the approximate factor models and call it a factor GARCH-Ito model. We then investigate its properties and propose a quasi-maximum likelihood estimation method for the parameter of the factor GARCH-Ito model. We also apply it to estimating conditional expected large volatility matrices and establish their asymptotic properties. Simulation studies are conducted to validate the finite sample performance of the proposed estimation methods. The proposed method is also illustrated by using data from the constituents of the S&P 500 index and an application to constructing the minimum variance portfolio with gross exposure constraints.

Keywords: Factor model, GARCH, low-rank, POET, quasi-maximum likelihood estimator, sparsity

JEL Classification: C13, C32, C53, C55, C58

Suggested Citation

Kim, Donggyu and Fan, Jianqing, Factor GARCH-ITO Models for High-Frequency Data with Application to Large Volatility Matrix Prediction (December 8, 2017). Available at SSRN: https://ssrn.com/abstract=3085735 or http://dx.doi.org/10.2139/ssrn.3085735

Donggyu Kim (Contact Author)

KAIST College of Business ( email )

85 Hoegiro Dongdaemun-Gu
Seoul 130-722, 130-722
Korea, Republic of (South Korea)

Jianqing Fan

Princeton University - Bendheim Center for Finance ( email )

26 Prospect Avenue
Princeton, NJ 08540
United States
609-258-7924 (Phone)
609-258-8551 (Fax)

HOME PAGE: http://orfe.princeton.edu/~jqfan/

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