Article by: Michael Parkinson
Published by: The Journal of Business
Date: 26 Feb 2009
“The random walk problem has a long history. In fact, its application to the movement of security prices predates the application to Brownian motion. And now it is generally accepted that, at least to a good approximation, ln (S), where S is the price of a common stock, follows a random walk. The diffusion constant characterizing that walk for each stock thus becomes an important quantity to calculate. In Section II, we describe the general random walk problem and show how the diffusion constant is traditionally estimated. In Section III, we discuss another way to estimate the diffusion constant, the extreme value method. In Section IV, we compare the traditional and extreme value methods and conclude that the extreme value method is about 21/2-5 times better, depending on how you choose to measure the difference. In Section V, we discuss the use of this method for the estimation of the variance of the rate of return of a common stock.”
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