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

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.