Modeling log-volatility with zero returns: Empirical evidence for asymmetric sv and log-garch models

Abstract

In this work, we address the challenges posed by zero returns in both stochastic volatility (SV) and log-GARCH models in their asymmetric form. Building upon Expectation-Maximization imputation for handling zero returns, we propose a unified approach that enhances parameter estimation robustness for both model classes. Specifically, we employ the Quasi-Maximum Likelihood estimation, incorporating the Kalman filter for both asymmetric SV and asymmetric log-GARCH models, to ensure robust parameter estimation even in the presence of zero returns. By comparing the performance of these models under our proposed framework, we provide new insights into their relative strengths in capturing the asymmetric volatility dynamics in the presence of zero returns. This contribution extends the existing literature by proposing a computational framework applicable to such models, based on a logarithmic specification of volatility.

Keywords: Kalman filter, Log-GARCH, Quasi-maximum likelihood, Stochastic volatility, Zero returns