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METHOD OF MOMENTS ESTIMATION FOR LÉVY-DRIVEN ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODELS

Published online by Cambridge University Press:  02 June 2020

Xiangyu Yang Open the ORCID record for Xiangyu Yang [Opens in a new window] ,
Yanfeng Wu ,
Zeyu Zheng Open the ORCID record for Zeyu Zheng [Opens in a new window]  and
Jian-Qiang Hu
Xiangyu Yang
Affiliation:
School of Management, Fudan University, Shanghai, China E-mail: xyyang19@fudan.edu.cn
Yanfeng Wu
Affiliation:
Jiangxi University of Finance and Economics, Nanchang, Jiangxi, China E-mail: wuyanfeng@jxufe.edu.cn
Zeyu Zheng
Affiliation:
Department of Industrial Engineering and Operations Research, University of California Berkeley, Berkeley, CA, USA E-mail: zyzheng@berkeley.edu
Jian-Qiang Hu
Affiliation:
School of Management, Fudan University, Shanghai, China E-mail: hujq@fudan.edu.cn
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Abstract

This paper studies the parameter estimation for Ornstein–Uhlenbeck stochastic volatility models driven by Lévy processes. We propose computationally efficient estimators based on the method of moments that are robust to model misspecification. We develop an analytical framework that enables closed-form representation of model parameters in terms of the moments and autocorrelations of observed underlying processes. Under moderate assumptions, which are typically much weaker than those for likelihood methods, we prove large-sample behaviors for our proposed estimators, including strong consistency and asymptotic normality. Our estimators obtain the canonical square-root convergence rate and are shown through numerical experiments to outperform likelihood-based methods.

Keywords

consistency and asymptotic normalitymethod of momentsparameter estimationstochastic volatility model
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 35 , Issue 4 , October 2021 , pp. 975 - 1004
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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