Continuous-time random-walk model for financial distributions

Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 1):021112. doi: 10.1103/PhysRevE.67.021112. Epub 2003 Feb 27.

Abstract

We apply the formalism of the continuous-time random walk to the study of financial data. The entire distribution of prices can be obtained once two auxiliary densities are known. These are the probability densities for the pausing time between successive jumps and the corresponding probability density for the magnitude of a jump. We have applied the formalism to data on the U.S. dollar-deutsche mark future exchange, finding good agreement between theory and the observed data.