Commonly, equilibrium security prices are modeled by continuous‐state stochastic processes, while observed prices are rounded into discrete units. This paper models the rounding mechanism and examines the probabilistic structure of the resultant rounded process. We provide accurate and simple estimates of the inflation in estimated variance and kurtosis induced by ignoring rounding. In particular, the maximum‐likelihood estimate of security price volatility using rounded prices is developed, and a simulation analysis is performed to examine the small‐sample properties of this estimator. For many practical applications, a simple correction for rounding becomes available.

Commonly, equilibrium security prices are modeled by continuous-state stochastic processes, while observed prices are rounded into discrete units. This paper models the rounding mechanism and examines the probabilistic structure of the resultant rounded process. We provide accurate and simple estimates of the inflation in estimated variance and kurtosis induced by ignoring rounding. In particular, the maximum-likelihood estimate of security price volatility using rounded prices is developed, and a simulation analysis is performed to examine the small-sample properties of this estimator. For many practical applications, a simple correction for rounding becomes available.

This paper introduces an event-study method that incorporates the possibility of a random event date. Consistent with empirical evidence, we assume an event may affect not only the conditional mean of a security's return, but also its conditional variance. We compare the statistical power and efficiency of our maximum-likelihood method with the standard application of traditional event-study methods to multiday security returns. Assuming a two-day event period, our empirical results provide evidence that the multiday approach is robust. We use our maximum-likelihood method to investigate the valuation effects of stock splits and stock dividends.