Detecting Arbitrage in the Foreign Exchange Market

In this paper, we propose a theoretical and computational framework for the detection and identification of (triangular) arbitrage opportunities among spot currency exchange rates in a foreign exchange market. We obtain sufficient conditions for excluding the triangular arbitrage opportunities in a market with or without market frictions, i.e. transaction costs. Then we propose a very efficient computational approach not only to detect triangular arbitrage opportunities in real time but also to identify the combinations of currencies that lead to the arbitrage opportunity from market data. In numerical studies, we utilize empirical data of foreign currency exchange rates to substantiate our theoretical findings and demonstrate the efficiency of the proposed computational approach