Stock arbitrage involves taking advantage of differences in prices of the same stock. The most common use of stock arbitrage is buying a stock on one market and selling it at another. In theory arbitrage will offer a guaranteed profit, but in reality, delays in transactions introduce an element of risk. It's also arguable that taking advantage of futures contracts or stock options can be classed as stock arbitrage.
The main meaning of arbitrage is to exploit price differences across markets. One example would be if a company's stock had a market price of $10 on the New York Stock Exchange and $15 on the Chicago Mercantile Exchange. In theory somebody buying the stock on the New York market and immediately selling it on the Chicago market would make a 50% profit.
There are some serious limitations to stock arbitrage. One is that the profit may be outweighed by transaction fees. Another is that even with electronic trading there may be a delay between buying on one market and selling on another, during which the price may change and wipe out the benefits.
The delay problems can happen particularly if a market is either very busy or very quiet. It the market is very busy, it is likely the price will be changing more rapidly than usual and thus at greater risk of changing unfavorably. If the market is very quiet, it may take some time to find a buyer for the stock, by which time the price may have fallen.
Carrying out stock arbitrage requires even closer attention than usual as two markets must be monitored. This problem is worsened by the fact that often the best opportunity for arbitrage comes with markets in different countries where the factors affecting the stock price may vary more widely. Attempting to carry out cross-border arbitrage means paying extra attention to exchange rates, to make sure the deal will work out profitably, and to time zones, to make sure both markets will remain open long enough to complete the deal.
Depending on the interpretation of the phrase, other stock activities can be considered arbitrage. A person who holds a futures contract or an options contract may be able to buy stock at a previously agreed price and immediately sell it at a higher price. Similarly, employees of a company that offers stock options as a benefit may be able to buy stock from the company and sell on the market at a higher price. Not everyone would class this as arbitrage, as some definitions insist it only applies in cases involving two separate markets.