Markovian approximation in foreign exchange markets

TL;DR

This paper tests the random walk hypothesis on high-frequency foreign exchange data and proposes a stochastic model that captures key features of market behavior, validated through correlation and information theory methods.

Contribution

It introduces a stochastic model for exchange rate variations that better describes market features than traditional assumptions.

Findings

Random walk hypothesis is challenged by high-frequency data.

The proposed model captures important market dynamics.

Information theory approaches validate the model's relevance.

Abstract

In this paper we test the random walk hypothesis on the high frequency dataset of the bid--ask Deutschemark/US dollar exchange rate quotes registered by the inter-bank Reuters network over the period October 1, 1992 to September 30, 1993. Then we propose a stochastic model for price variation which is able to describe some important features of the exchange market behavior. Besides the usual correlation analysis we have verified the validity of this model by means of other approaches inspired by information theory . These techniques are not only severe tests of the approximation but also evidence some aspects of the data series which have a clear financial relevance.