A GMM approach for estimation of volatility and regression models when daily prices are subject to price limits

In this paper, we derive a generalized method of moments (GMM) estimator for variance in markets with daily price limits. We compare the GMM estimator with the maximum likelihood (ML) estimator and three ad hoc estimators used in the literature. All three ad hoc estimators are downward-biased. Furthermore, when the normality assumption is violated, the ML estimator becomes biased. Simulation results confirm our theoretical predictions. Given the evidence that daily returns are non-normal for most financial assets and the fact that the GMM estimator is much simpler than the ML estimator to implement, it is recommended that the GMM estimator be used in real applications. Finally, the extension of the GMM estimator to regression models is also discussed. We find that the GMM estimator for regression models is equivalent to the instrumental-variables (IV) estimator.