# Triangular Arbitrage

Triangular Arbitrage

Suppose you are a trader at the foreign exchange desk of Goldman Sachs in London and you observe the following exchange rates of the Euro (EUR) relative to the pound (GBP) and the U.S. Dollar (USD) and the USD relative to GBP:

Quote Currency/Base Currency Rate

EUR/GBP                                                 1.1555

EUR/USD                                                    0.76388

USD/GBP                                                    1.5386

Recall that the base currency is the currency that is being purchased or sold and the quote currency is the price. Thus, if EUR/GBP is equal to 1.1555, then it costs 1.1555 EUR to buy 1 GBP (or I can sell 1 GBP for 1.1555 EUR).

Triangular arbitrage is the act of exploiting an arbitrage opportunity resulting from a pricing discrepancy among three dierent currencies in the foreign exchange market. A triangular arbitrage strategy involves three trades, exchanging the initial currency for a second, the second currency for a third, and the third currency for the initial. During the second trade, the arbitrageur locks in a zero-risk prot from the discrepancy that exists when the market cross exchange rate is not aligned with the implicit cross exchange rate.