Estimation Bias Induced by Discrete Security Prices

  • Author(s): CLIFFORD A. BALL
  • Published: Apr 30, 2012
  • Pages: 841-865
  • DOI: 10.1111/j.1540-6261.1988.tb02608.x


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.

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