Handbook of Heavy Tailed Distributions in Finance

Chapter 1

Heavy Tails in Finance for Independent or Multifractal Price Increments

Benoit B. Mandelbrot    Sterling Professor of Mathematical Sciences, Yale University, New Haven, CT 065020-8283, USA

Abstract

This chapter has two goals. Section 1 sketches the history of heavy tails in finance through the author’s three successive models of the variation of a financial price: mesofractal, unifractal and multifractal. The heavy tails occur, respectively, in the marginal distribution only (Mandelbrot, 1963), in the dependence only (Mandelbrot, 1965), or in both (Mandelbrot, 1997). These models increase in the scope of the “principle of scaling invariance”, which the author has used since 1957.

The mesofractal model is founded on the stable processes ...