Arbitrage detection using max plus product iteration on foreign exchange rate graphs

We propose a novel graph-theoretic method to detect k-currency arbitrage in spot foreign exchange (FX) markets and discuss and compare the runtime performance of this method against the permutation search approach. This technique is applied to a minute level bid/ask quote dataset consisting of rates constructed from all G10 currency pairs. We validate this approach through an example while also demonstrating its runtime efficiency, especially in the case of spot markets consisting of a large number of currency pairs. Finally, several potential extensions including trading applications are discussed.