Turbulent Behavior of Stock Exchange Indices and Foreign Currency Exchange Rates

Abstract

The time evolution of stock exchange indices and foreign currency exchange rates has many similarities with turbulent flows. In particular, the probability densities of price changes are non-Gaussian and develop stretched exponential tails, quite similar to the densities of velocity differences measured in fully developed hydrodynamical turbulence. We show that a simple cascade model, based on a self-similar, hierarchical dynamics of price changes, describes the observed probability densities of the financial indices in a quantitatively correct way.