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

Abstract 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.

[1]  R. Oomen,et al.  Internalisation by electronic FX spot dealers , 2018, Quantitative Finance.

[2]  Uri Zwick,et al.  All pairs shortest paths using bridging sets and rectangular matrix multiplication , 2000, JACM.

[3]  Ryan Williams,et al.  Faster all-pairs shortest paths via circuit complexity , 2013, STOC.

[4]  Lucio Sarno,et al.  Arbitrage in the Foreign Exchange Market: Turning on the Microscope , 2006 .

[5]  R. Gencay,et al.  A New Wavelet-based Ultra-High-Frequency Analysis of Triangular Currency Arbitrage , 2019, Economic Modelling.

[6]  Spot Arbitrage in FX Market and Algorithmic Trading: Speed is Not of the Essence , 2019 .

[7]  Magnus Aarheim,et al.  High frequency arbitrage in foreign exchange markets , 2014 .

[8]  N. Gradojevic.  Frequency domain analysis of foreign exchange order flows , 2012 .

[9]  James B. Orlin,et al.  An O(nm) time algorithm for finding the min length directed cycle in a graph , 2016, SODA.

[10]  Tarun Ramadorai,et al.  What determines transaction costs in foreign exchange markets , 2008 .

[11]  Nikola Gradojevic,et al.  Informativeness of trade size in foreign exchange markets , 2017 .

[12]  Ronald W. Masulis,et al.  FX Spreads and Dealer Competition Across the 24-Hour Trading Day , 1999 .

[13]  Neil F. Johnson,et al.  The Mirage of Triangular Arbitrage in the Spot Foreign Exchange Market , 2008, 0812.0913.

[14]  Roman Kozhan,et al.  Execution Risk in High-Frequency Arbitrage , 2012, Manag. Sci..

[15]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.