Commonly, equilibrium security prices are modeled by continuous state stochastic processes while observed prices are rounded i nto discrete units. This paper models the rounding mechanism and exam ines the probabilistic structure of the resultant rounded process. Th e author provides accurate and simple estimates of the inflation in e stimated variance and kurtosis induced by ignoring rounding. In parti cular, the maximum likelihood estimate of security price volatility, using rounded prices, is developed and a simulation analysis is perfo rmed to examine the small sample properties of this estimator. For ma ny practical applications, a simple correction for rounding becomes a vailable. Copyright 1988 by American Finance Association.