Since the number of transactions in any time period is random, different distributions are needed to represent price changes over fixed numbers of transactions and fixed time periods. It appears that the former follow a Gaussian distribution, while the latter follow a L-stable distribution. M & Taylor 1967 shows that those two distributions are by no means contratictory: a scenario based on a fractal subordination time is proposed by Taylor (Section 1), then shown by Mandelbrot (Section 2) to be intimately related to an earlier discussion of the specialists’ function of “ensuring the continuity of the market.” Note that this scenario is only compatible with the M 1963 model restricted to a symmetric distribution of price changes. Section 3 — reproducing M 1973c — elaborates by responding to Clark 1973.
KeywordsStock Price Price Change Fractal Time Infinite Variance Sample Moment
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