On the Distribution of Stock Price Differences

Abstract

Price changes over a fixed number of transactions may have a Gaussian distribution. Price changes over a fixed time period may follow a stable Paretian distribution, whose variance is infinite. Since the number of transactions in any time period is random, the above statements are not necessarily in disagreement. A possible explanation is proposed by Taylob, and then shown by Mandelbrot to be intimately related to an earlier discussion of the specialists' function of ensuring the continuity of the market.