To find out if arbitrage opportunity exists, I calculated the same currency pair using GBP:USD and GBP:EUR and resulted in 0.7055 - 0.7065. So there is an arbitrage opportunity here.
The answer for the arbitrage profit is $6372
USD –> EUR –> GBP –> USD? (0.7000/1.2010) x 1.7000 = $0.9908, I have a loss here.
USD –> GBP –> EUR –> USD? (1.2000/1.7010) x (1/0.7010) = $1.006372. I have a gain $6372
you have to ask youserlf in term of the domestic currency USD ,which one will give you more in term of the other currency when your are looking at the misspriced quote :
you can get it directly 700 000Eur with the direct quote 0.7000 - 0.7010
or you can get 705 500Eur by strating up with GBP and doing the triangle 0.7055 - 0.7065
so you always want to get more. if the quote was over quote, then you would start with the one that pays more. which would be the direct quote and do the inverse triangle
I think this answers it. I never focused on the the inverse triange value 0.7055 - 0.7065, except to find out if arbitrage is possible or not. So I know upfont now, that I am getting 0.7055 EUR/USD using the inverse triangle. If the inverse quote is less (say 0.6055 - 65), then I should avoid this route and start with 0.7000 - 0.7010.
Like some have commented I only worked out if possible OR not. I would use the ladder approach, bid and ask column then place your FX pairs underneath each other - 3 in total, starting and ending pair should have the currency that’s in the nominal amount. Obviously you may need to take the inverse etc to make that happen.
borrowing in USD.
USD/NZD
USD/GBP
EUR/GBP
____
BID ASK
1 1
USD/ NZD
EUR/GBP
GBP/USD
if you are on the bid, move up the bid so multiply, or down the ask so divide down the FX pairs in each column. if < 1 then no arbitrage exists, if > 1 then it does.