Crossposed on Quantitative Finance SE
I was able to solve this 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? here is the question and my answer The dealers A and B use the following rates for currency exchange: $$ \begin{matrix} dealer-A & BUY & SELL \\ EUR-1 & USD-1.018 & USD-1.0284 \\ GBP-1 & USD-1.5718 & USD-1.5944 \\ \end{matrix} $$ $$ \begin{matrix} dealer-B & BUY & SELL \\ EUR-1 & GBP-0.6354 & GBP-0.6401 \\ USD-1 & GBP-0.6309 & GBP-0.6375 \\ \end{matrix} $$
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)
Got 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.
You can write a quick program to calculate the triangular arbitrage with all bid and ask exchange prices. It should not be that difficult to find the arbitrage in seconds. Always a (bid, ask, bid) except that you have two dealers instead of three dealers. When I have time I shall write a program and see if I could get the arbitrage in seconds.
This is not an answer but a hint.