Currency arbitrage is when the value of a triangle of currency pairs does not cross-correlate, and a bank or large institution is able to exploit the temporary discrepancy for a profit before the market equalizes again.
Arbitrage is when an investor (usually an institutional investor) can pick up something in one market that has a higher value in another market, perhaps due to lower liquidity or information flow in the secondary market, and can move goods or securities across these markets and make a profit.
The cost of transferring the goods or securities from one market to the other must be lower than the spread between the two values. Currency arbitrage requires three currency pairs to be out of sync, called triangular arbitrage.
Let’s say the three currencies in question are dollars (USD), euros (EUR), and pounds (GBP). One day the dollar appreciates relative to the pound but there is no movement in the USD/EUR exchange rate yet. The arbitrageur could exploit the triangle and exchange USD for EUR, then EUR for GBP, then GBP for USD.
This would be a risk-free profit if the trader could execute all of the trades nearly instantaneously. These arbitrage opportunities will pretty much never present themselves to the average investor, since large banking institutions are monitoring the Forex markets closely at all times and could act on it more quickly, with large amounts of money, and this would cause the opportunity gap to close, as the exchange rates would be brought into equilibrium.