Exponential GARCH-Ito Volatility Models

TL;DR

This paper proposes the exponential realized GARCH-Ito (ERGI) model, a novel continuous-time volatility model that integrates non-linear GARCH dynamics with high-frequency data, offering improved modeling of financial volatility.

Contribution

It introduces a non-linear structure for instantaneous volatility in a continuous-time model, linking discrete GARCH dynamics with high-frequency data analysis.

Findings

The ERGI model captures volatility dynamics more accurately.

Simulation results demonstrate the model's good finite sample performance.

Empirical analysis shows advantages over existing models.

Abstract

This paper introduces a novel Ito diffusion process to model high-frequency financial data, which can accommodate low-frequency volatility dynamics by embedding the discrete-time non-linear exponential GARCH structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Ito models, the instantaneous volatility process has a non-linear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Ito (ERGI) model. Given the auto-regressive structure of the log-integrated volatility, we propose a quasi-likelihood estimation procedure for parameter estimation and establish its asymptotic properties. We conduct a simulation study to check the finite sample performance of the proposed model and an empirical study with 50 assets among the S\&P 500 compositions. The numerical studies show the advantages of the new proposed model.