Overview

Arbitrage (/ˈɑːrbɪtrɑːʒ/ ^(ⓘ), UK also /-trɪdʒ/) is the practice of taking advantage of a difference in prices in two or more markets – striking a combination of matching deals to capitalize on the difference, the profit being the difference between the market prices at which the unit is traded. Arbitrage has the effect of causing prices of the same or very similar assets in different markets to converge.

When used by academics in economics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit after transaction costs. For example, an arbitrage opportunity is present when there is the possibility to instantaneously buy something for a low price and sell it for a higher price.

In principle and in academic use, an arbitrage is risk-free; in common use, as in statistical arbitrage, it may refer to expected profit, though losses may occur, and in practice, there are always risks in arbitrage, some minor (such as fluctuation of prices decreasing profit margins), some major (such as devaluation of a currency or derivative).

In academic use, an arbitrage involves taking advantage of differences in price of a single asset or identical cash-flows; in common use, it is also used to refer to differences between similar assets (relative value or convergence trades), as in merger arbitrage.

Etymology

"Arbitrage" is a French word and denotes a decision by an arbitrator or arbitration tribunal (in modern French, "arbitre" usually means referee or umpire). It was first defined as a financial term in 1704 by French mathematician Mathieu de la Porte in his treatise "La Science des négociants et teneurs de livres" as a consideration of different exchange rates to recognise the most profitable places of issuance and settlement for a bill of exchange ("L'arbitrage est une combinaison que l'on fait de plusieurs changes, pour connoitre [connaître, in modern spelling] quelle place est plus avantageuse pour tirer et remettre".)

Arbitrage equilibrium

If the market prices do not allow for profitable arbitrage, the prices are said to constitute an arbitrage equilibrium, or an arbitrage-free market. An arbitrage equilibrium is a precondition for a general economic equilibrium. The 'no-arbitrage assumption' is used in quantitative finance to calculate a unique risk neutral price for derivatives.

Arbitrage-free pricing approach for bonds

Arbitrage-free pricing for bonds is the method of valuing a coupon-bearing financial instrument by discounting its future cash flows by multiple discount rates. By doing so, a more accurate price can be obtained than if the price is calculated with a present-value pricing approach. Arbitrage-free pricing is used for bond valuation and to detect arbitrage opportunities for investors.

For the purpose of valuing the price of a bond, its cash flows can each be thought of as packets of incremental cash flows with a large packet upon maturity, being the principal. Since the cash flows are dispersed throughout future periods, they must be discounted back to the present. In the present-value approach, the cash flows are discounted with one discount rate to find the price of the bond. In arbitrage-free pricing, multiple discount rates are used.

The present-value approach assumes that the bond yield will stay the same until maturity. This is a simplified model because interest rates may fluctuate in the future, which in turn affects the yield on the bond. For this reason, the discount rate may differ for each cash flow. Each cash flow can be considered a zero-coupon instrument that pays one payment upon maturity. The discount rates used should be the rates of multiple zero-coupon bonds with maturity dates the same as each cash flow and similar risk as the instrument being valued.

By using multiple discount rates, the arbitrage-free price is the sum of the discounted cash flows. Arbitrage-free price refers to the price at which no price arbitrage is possible.

Conditions for arbitrage

Arbitrage is not simply the act of buying a product in one market and selling it in another for a higher price at some later time. The transactions must occur simultaneously to avoid exposure to market risk, or the risk that prices may change in one market before both transactions are complete. In practical terms, this is generally possible only with securities and financial products that can be traded electronically, and even then, when each leg of the trade is executed, the prices in the market may have moved.

Missing one of the legs of the trade (and subsequently having to trade it soon after at a worse price) is an 'execution risk' referred to as 'leg risk'.

In the simplest example, any good sold in one market should sell for the same price in another. Traders may, for example, find that the price of wheat is lower in agricultural regions than in cities, purchase the good, and transport it to another region to sell at a higher price. This type of price arbitrage is the most common, but this simple example ignores the cost of transport, storage, risk, and other factors. "True" arbitrage requires that there is no market risk involved.

Where securities are traded on more than one exchange, arbitrage occurs by simultaneously buying in one and selling on the other.

See rational pricing, particularly § arbitrage mechanics, for further discussion.