According to the Law of One Price, equivalent assets (i.e., assets with the same payoff) must have the same price (see, e.g., Bodie & Merton 1998). In competitive markets, the price of an asset must be the same worldwide providing that it is expressed in the same currency, and the transportation and transaction costs can be neglected. Violation of the Law of One Price leads to arbitrage, which is risk-free profiteering by buying an asset in a cheaper market and immediately selling it in a more expensive market.
In FX, a typical example of arbitrage is so-called triangle arbitrage. It appears in case of imbalance among three related currency pairs. Namely, exchange rates for three currencies X, Y, and Z generally satisfy the condition
An arbitrage opportunity appears if (11.1) is violated. For example, if the product (EUR/JPY)*(USD/EUR) is smaller than USD/JPY, one can buy JPY with USD, then buy EUR with JPY, and finally, make profits by buying USD for EUR.1
Arbitrage can continue only for a limited time until mispricing is eliminated due to increased demand and finite supply of a cheaper asset.2 Such a clear-cut (deterministic) opportunity, which guarantees a riskless gain, is sometimes called pure arbitrage (Bondarenko 2003). Deterministic arbitrage should be discerned from statistical arbitrage, which is based on statistical deviations of ...