Triangular Arbitrage and Cross-Currency Correlations in an Agent-Based FX Model

Summary

This study uses an agent-based model to explore how correlations between exchange rates can arise in foreign exchange markets. It focuses on interactions between market makers and an arbitrager exploiting triangular price relationships. The motivation is that related currency pairs can move together over very short periods, with unusually large synchronized moves becoming apparent during events such as flash crashes.

The model qualitatively reproduces patterns linking correlation strength to the time scale, as observed in trading data. Its results suggest that triangular arbitrage is an important source of linked dynamics across rates. The model also indicates that the sign and magnitude of correlations between two exchange rates depend on how triangular arbitrage interacts with trend-following strategies. These are model-based explanations rather than proof of the causal mechanism in live markets: the excerpt does not describe calibration, quantitative fit, or trading performance. Its contribution is to propose a microscopic account of cross-currency dependence, not a ready-to-trade arbitrage strategy.

Key ideas

• The model studies how market makers and a triangular arbitrager interact to generate currency-pair correlations.
• It qualitatively reproduces the observed relationship between correlation patterns and time scale.
• The results point to triangular arbitrage as a driver of linked exchange-rate dynamics.
• Trend-following behavior affects the sign and strength of correlations between currency pairs.
• The findings explain model behavior but do not establish a profitable live-trading strategy.

Tags

# 2002.02583


# 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.

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