  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.
