Modeling of waiting times and price changes in currency exchange data

TL;DR

This paper extends a continuous-time random walk model for financial data by incorporating dependence between waiting times and price returns, using a Lévy stable distribution, and demonstrates improved data fitting for exchange and stock data.

Contribution

It introduces a generalized model that accounts for dependence between waiting times and returns, enhancing the fit to real financial data over previous models.

Findings

Improved chi-squared fit to exchange rate data

Better modeling of waiting times and returns

Enhanced accuracy over traditional models

Abstract

A theory which describes the share price evolution at financial markets as a continuous-time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function (pdf) which uses the concept of a L\'{e}vy stable distribution is worked out. The theory is fitted to high-frequency US$/Japanese Yen exchange rate and low-frequency 19th century Irish stock data. The theory has been fitted both to price return and to waiting time data and the adherence to data, in terms of the chi-squared test statistic, has been improved when compared to the old theory.