Editing Arbitrage (section)

==Conditions for arbitrage==
Arbitrage may take place when:

* the same asset does not trade at the same price on all markets ("[[law of one price|the law of one price]]").

* two assets with identical cash flows do not trade at the same price.

* an asset with a known price in the future does not today trade at its future price [[Discounting|discounted]] at the [[risk-free interest rate]] (or the asset has significant costs of storage; so this condition holds true for something like grain but not for [[security (finance)|securities]]).

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. [[Merchant|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 [[rational pricing#Arbitrage mechanics|§ arbitrage mechanics]], for further discussion.

Mathematically it is defined as follows:

: <math>P(V_t \geq 0) = 1 \text{ and } P(V_t \neq 0) > 0, \,0<t\le T</math>

where <math>V_0 = 0</math>, <math>V_t</math> denotes the portfolio value at time&nbsp;''t'' and ''T'' is the time the portfolio ceases to be available on the market. This means that the value of the portfolio is never negative, and guaranteed to be positive at least once over its lifetime.

Negative, or anti-, arbitrage is similarly defined as

: <math>P(V_t \leq 0) = 1 \text{ and } P(V_t \neq 0) > 0, \,0<t\le T</math>

and occurs naturally in arbitrage relations as the seller view as opposed to the buyer view.