The Black Swan: The Impact of the Highly Improbable · chapter 2 · id the-black-swan-c2-05-mandelbrot-discovered-in-1963-
“Mandelbrot discovered in 1963 that cotton price variations follow a Levy-stable distribution with parameter alpha of approximately 1.7, not the Gaussian distribution (alpha = 2), meaning infinite variance and much fatter tails than standard models assume.”
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Receipts
Mandelbrot (1963), 'The Variation of Certain Speculative Prices', Journal of Businesssource alive
Mandelbrot found cotton prices followed a Levy stable distribution with parameter alpha equal to 1.7 rather than 2 as in a Gaussian distribution. The Pareto-Levy distribution has infinite variance, implying extreme market moves contribute significantly to overall evolution.
Wikipedia: Benoit Mandelbrotsource alive
In 1963, Mandelbrot proposed that cotton price changes followed Levy stable distributions rather than Gaussian distributions, based on analysis of price data from 1900 to 1960.
Cont (2024), 'Benoit Mandelbrot in Finance', HAL Archivessource alive
Mandelbrot's 1963 paper demonstrated that price changes exhibit self-similarity across time scales and follow distributions with much heavier tails than Gaussian models predict. Subsequent research confirmed fat tails in financial data while debating the specific distributional f
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