Estimating the Volatility of Discrete Stock Prices




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    • School of Business and Departmento f Statistics, University of Wisconsin-MadisonA. n earlier version of this paper has been presented at Boston University, Columbia University, Merrill Lynch, Northwestern University, Purdue University, Southern Methodist University, University of California-Riverside, University of Illinois, University of Southern California, University of Wisconsin-Madison, Vanderbilt University, the Actuarial Research Conference in Toronto, the European Finance Association Meetings in Madrid, and the American Finance Association Meetings in Chicago. We would like to thank participants of these workshops. We also would like to thank Lillyn Teh for her computational assistance.


This paper introduces an estimator of stock price volatility that eliminates, at least asymptotically, the biases that are caused by the discreteness of observed stock prices. Assuming that the observed stock prices are continuously monitored, an estimator is constructed using the notion of how quickly the price changes rather than how much the price changes. It is shown that this estimator has desirable asymptotic properties, including consistency and asymptotic normality. Also, through a simulation study, the authors show that it outperforms natural estimators for the low- and middle-priced stocks. Furthermoret, he simulation study demonstratest hat the proposed estimator is robust to certain misspecifications in measuring the time between price changes.