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Foreign exchange rates movements exhibit significant cross-correlations evenon very short time-scales. The effect of these statistical relationships becomeevident during extreme market events, such as flash crashes.In this scenario,an abrupt price swing occurring on a given market is immediately followed byanomalous movements in several related foreign exchange rates. Although a deepunderstanding of cross-currency correlations would be clearly beneficial forconceiving more stable and safer foreign exchange markets, the microscopicorigins of these interdependencies have not been extensively investigated. Weintroduce an agent-based model which describes the emergence of cross-currencycorrelations from the interactions between market makers and an arbitrager. Ourmodel qualitatively replicates the time-scale vs. cross-correlation diagramsobserved in real trading data, suggesting that triangular arbitrage plays aprimary role in the entanglement of the dynamics of different foreign exchangerates. Furthermore, the model shows how the features of the cross-correlationfunction between two foreign exchange rates, such as its sign and value, emergefrom the interplay between triangular arbitrage and trend-following strategies.

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