Currency Arbitrage

Currency arbitrage is the exploitation of price discrepancies across markets to generate risk-free profit by buying low in one venue and selling high in another. In the foreign exchange market, arbitrage opportunities arise when cross-rates between currency pairs are inconsistent: if EUR/USD × USD/JPY ≠ EUR/JPY, a triangular arbitrage exists. These discrepancies are typically small and short-lived, detected and eliminated within milliseconds by algorithmic trading systems, but their existence is theoretically significant: they represent violations of the law of one price that efficient markets are supposed to enforce.

The detection of arbitrage opportunities maps directly onto the Bellman-Ford algorithm's negative-cycle detection. Treating exchange rates as edge weights in a graph of currencies, a negative cycle corresponds to an arbitrage loop: a sequence of conversions that returns more of the original currency than it started with. This structural isomorphism reveals that arbitrage is not merely a financial phenomenon but a general property of weighted networks: wherever relative valuations are inconsistent, opportunities for cyclic extraction exist. The same mathematics underlies detection of tax loopholes, supply chain inefficiencies, and regulatory arbitrage in institutional design.