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.
Determine the arbitrage prots if you start with 10,000,000 EUR and buy GBP.
