Method of Moments Estimation for Lévy-driven Ornstein-Uhlenbeck Stochastic Volatility Models

Zeyu Zheng, Xiangyu Yang, Yanfeng Wu, and Jian-Qiang Hu. Method of Moments Estimation for Lévy-driven Ornstein-Uhlenbeck Stochastic Volatility Models. Probability in the Engineering and Informational Sciences. https://doi.org/10.1017/S0269964820000315.

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.