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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.

Rodrigo de Azevedo
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idknuttin
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1 Answers1

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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.

Satish Ramanathan
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  • Yes but wouldn't it take almost just as long trying to write a program as exhausting every option? – idknuttin Feb 08 '16 at 14:05
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    Yes it may take longer, but if done, you can call it million times just by changing the data. You really do not know if there are other lucrative arbitrages than this if you have not tried all currencies. Quick and dirty method would be try starting currency set the triangular arbitrage with Bid-ask-bid combo, you may succeed quickly. – Satish Ramanathan Feb 08 '16 at 14:41