Mathematical Finance Seminar
October 4, 2001 , 5:30 PM to 7:00 PM
Benoit Mandelbrot, Yale University
The multifractal model of financial prices: long dependence and scaling invariance
An acknowledged feature of financial prices is that, compared to
Gaussianity and independence or Markovian behavior, their variability is
extremely "anomalous." The speaker responded with a power-law relative to
long-tailedness (1963; the first economist to follow up was E.F. Fama) and
a power-law relative to infinite dependence (1965; the first economist to
follow up was C.W.J. Granger). Both power-laws are consequences of very
simple principles of scale invariance. In this talk it will be shown that
a generalized form of scale invariance leads to the multifractal models, in
which long-tails and long-dependence, are automatically combined.