# Is there an efficient method or technique to find an arbitrage between two FX dealers?

I was able to solve the following problem and find the arbitrage but only after spending a long time on it and trying out different possibilites. Is there a method or technique that can help me find the arbitrage faster and in a more efficient way rather than just trying out different possibilites?

Dealers $$A$$ and $$B$$ use the following exchange rates:

$$\begin{array}{l|l|l} \text{dealer } A & \text{Buy} & \text{Sell} \\\hline \text{EUR } 1 & \text{USD } 1.018 & \text{USD } 1.0284 \\ \text{GBP } 1 & \text{USD } 1.5718 & \text{USD } 1.5944 \\ \end{array}$$

$$\begin{array}{l|l|l} \text{dealer } B & \text{Buy} & \text{Sell} \\\hline \text{EUR } 1 & \text{GBP } 0.6354 & \text{GBP } 0.6401 \\ \text{USD } 1 & \text{GBP } 0.6309 & \text{GBP } 0.6375 \\ \end{array}$$

Find an arbitrage opportunity.

• Borrow 1 British pound (GBP)

• Go to dealer B and exchange your pounds for euros (1.5623 euros)

• Go to dealer A and exchange euros for dollars (1.5904)

• Go to dealer B and exchange dollars to pounds (1.0034 pounds)

• Return the 1 pound you borrowed and you just made 0.0034 pounds

There is an arbitrage of 0.0034 pounds.

• It could be reduced to a directed graph, but you would still have to try every loop in the graph to see if it earns a profit. – Alex C Feb 7 '16 at 22:15
• Is that a real life example? If so ... Are you taking into account transaction costs on that calculation? Including withdrawal costs from dealers? Also, are you sure that both dealers quote the currencies without delay and lock-in the rate once the order is placed? – phdstudent Feb 7 '16 at 22:55
• The transaction cost is the bid-ask spread, so it is taken into account already – Alex C Feb 7 '16 at 23:29
• @volcompt this is just a simple question from my financial mathematics class, not a real life example – idknuttin Feb 7 '16 at 23:56
• fatvat.co.uk/2010/07/foreign-exchange-arbitrage.html – Rodrigo de Azevedo Oct 6 '16 at 23:21