Circular Arbitrage Detection Using Graphs

We propose a novel graph-theoretic method for the detection of circular arbitrage in foreign exchange (FX) markets and discuss and demonstrate runtime improvements of this algorithm over the brute force approach. An application on empirical currency bid/ask price data validates this technique as well as provides an example of increased computational efficiency, especially in the case where a large number of currencies are considered. Using minute level market data for all G10 currency pairs, we demonstrate the efficiency of the algorithm as well as potential returns of higher order circular arbitrage trades. Finally, several potential extensions are discussed.