A Multifractal Model of Asset Returns

The probabilistic description of financial prices, pioneered by Bachelier (1900), initially focused onindependent and Gaussian distributed price changes. Financial economists have long recognizedtwo major discrepancies between the Bachelier model and actual financial data. First, financialdata commonly display temporal dependence in the alternation of periods of large price changeswith periods of smaller changes. Secondly, the tails of the histogram of observed data are typicallymuch fatter than predicted by the Gaussian distribution.