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I am very confused about what two currencies are to be chosen as the cross rate in a triangular arbitrage.

For example, when the bank quotes are

  1. ¥180/£

  2. $1.5/£

  3. ¥130/$

Does the cross rate have to be ¥120/$?

Couldn't it be $1.38/£?

Can I use any two currencies to calculate the profit?

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  • $\begingroup$ It doesn’t matter which rate you treat as the ‘cross rate’ in the same way that there is no one side of a triangle which is more important than the other two. $\endgroup$
    – Chris Taylor
    Commented Dec 29, 2018 at 21:31

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Any 2 rates imply the third.

Now what is missing here is that you did not provide actual quotes. A quote is the given of a bid and offer values. If you don’t know each dealer’s bid and offer there is no way to assert whether the levels offer an arbitrage opportunity or not. You could see an implied 1.38 level against a fair value of 1.5 however if the bid/offer half-spread is say 0.2 then this spread opportunity would not be a real one as the expected gross profit would be less than transaction costs.

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