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EXPONENTIAL REALIZED GARCH-ITÔ VOLATILITY MODELS

Published online by Cambridge University Press:  10 November 2022

Donggyu Kim Open the ORCID record for Donggyu Kim [Opens in a new window]
Donggyu Kim*
Affiliation:
College of Business, Korea Advanced Institute of Science and Technology (KAIST)
*
Address correspondence to Donggyu Kim, College of Business, Korea Advanced Institute of Science and Technology (KAIST), Seoul, South Korea; e-mail: donggyukim@kaist.ac.kr.
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Abstract

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This paper introduces a novel Itô diffusion process to model high-frequency financial data that can accommodate low-frequency volatility dynamics by embedding the discrete-time nonlinear exponential generalized autoregressive conditional heteroskedasticity (GARCH) structure with log-integrated volatility in a continuous instantaneous volatility process. The key feature of the proposed model is that, unlike existing GARCH-Itô models, the instantaneous volatility process has a nonlinear structure, which ensures that the log-integrated volatilities have the realized GARCH structure. We call this the exponential realized GARCH-Itô model. Given the autoregressive 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. Numerical studies show the advantages of the proposed model.

Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 4 , August 2024 , pp. 790 - 826
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

The author thanks the Editor (Professor Peter C.B. Phillips), the Co-Editor (Professor D. Kristensen), and anonymous two referees for their careful reading of this paper and valuable comments. The research of the author was supported in part by the National Research Foundation of Korea (NRF) (2021R1C1C1003216).

References

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