This paper examines the problem of estimating capital asset price volatility parameters from the most available forms of public data. While many varieties of such data are possible, we shall consider here only those which are truly universal in their accessibility to investors, namely, data appearing in the financial pages of the newspaper. In particular, we shall consider volatility estimators which are based upon the historical opening, closing, high, and low prices and transaction volume. Alternative estimators of volatility may be constructed from such data as significant news events, "fundamental" information regarding a company's prospects, and other forms of publicly available data, but these will not be considered here. Any parameter-estimation procedure must begin with a maintained hypothesis regarding the structural model within which estimation is to be made. Our structural model is given exposition in Section II. Section III discusses the "classical" Improved estimators of security price volatilities are formulated. These estimators employ data of the type commonly found in the financial pages of a newspaper: the high, low, opening, and closing prices and the transaction volume. The new estimators are seen to have relative efficiencies that are considerably higher than the standard estimators.