The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets

TL;DR

This paper presents an agent-based model that explains how triangular arbitrage influences short-term cross-currency correlations in forex markets, especially during extreme events like flash crashes.

Contribution

It introduces a microscopic agent-based model that reproduces real-world cross-currency correlation patterns and highlights the role of triangular arbitrage in these dynamics.

Findings

Model qualitatively replicates real cross-correlation diagrams

Triangular arbitrage significantly impacts currency rate entanglement

Features of cross-correlation functions emerge from arbitrage and trend strategies

Abstract

Foreign exchange rates movements exhibit significant cross-correlations even on very short time-scales. The effect of these statistical relationships become evident during extreme market events, such as flash crashes.In this scenario, an abrupt price swing occurring on a given market is immediately followed by anomalous movements in several related foreign exchange rates. Although a deep understanding of cross-currency correlations would be clearly beneficial for conceiving more stable and safer foreign exchange markets, the microscopic origins of these interdependencies have not been extensively investigated. We introduce an agent-based model which describes the emergence of cross-currency correlations from the interactions between market makers and an arbitrager. Our model qualitatively replicates the time-scale vs. cross-correlation diagrams observed in real trading data, suggesting that triangular arbitrage plays a primary role in the entanglement of the dynamics of different foreign exchange rates. Furthermore, the model shows how the features of the cross-correlation function between two foreign exchange rates, such as its sign and value, emerge from the interplay between triangular arbitrage and trend-following strategies.