A continuous time random walk model for financial distributions

TL;DR

This paper introduces a continuous time random walk model to describe financial price distributions, linking the entire distribution to two auxiliary densities and validating it with US dollar/Deutsche Mark futures data.

Contribution

The paper applies the continuous time random walk formalism to financial data, providing a new way to model price distributions based on pausing times and jump magnitudes.

Findings

Good agreement between model and observed data

Model accurately captures the distribution of exchange rate returns

Provides a framework for analyzing financial time series

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 US dollar/Deutsche Mark future exchange, finding good agreement between theory and the observed data.