University of Guilan Journal of Mathematical Modeling 2345-394X 14 2 2026 05 01 Modeling log-volatility with zero returns: empirical evidence for asymmetric SV and log-GARCH models 787 801 9400 10.22124/jmm.2026.31979.2889 EN Abdeljalil Settar Laboratory of mathematics, computer science and applications (LMCSA), FST Mohammedia, Hassan II university, 20650 Casablanca, Morocco Sara Chegdal Laboratory of mathematics, computer science and applications (LMCSA), FST Mohammedia, Hassan II university, 20650 Casablanca, Morocco Mustapha Kabil Laboratory of mathematics, computer science and applications (LMCSA), FST Mohammedia, Hassan II university, 20650 Casablanca, Morocco Ghassane Benrhmach Department of Mathematics and Statistics, College of Engineering, Abu Dhabi University, 59911 Abu Dhabi, UAE Journal Article 2025 10 15 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 EM 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 (QML) 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. https://jmm.guilan.ac.ir/article_9400_bd9ba5bd36544b3dee3440a32fed3017.pdf