A binary option is a contract between two parties in which one party (the buyer) pays the other party (the seller) and in return the seller will pay the buyer a fixed amount of money (or some other asset) if a specified event happens. The event can be anything, but with financial products it is usually based on the price of some security or index at some point in time in the future. Some examples:
Will the Dow Jones Industrial Average be above 15,000 when the market closes on June 30, 2013?
In ten minutes will the price of Apple stock be higher than it is right now?
In all cases it must possible to answer the question with an answer of yes or no. The terms of the contract must give an unambiguous way that the question will be answered.
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I have seen two primary types of binary options. One type is a private company that sells the binary options for a fixed price to the public. For example, they may charge you $10 per option and pay you $17 if the event occurs. These sites almost always have very short term options, Buying options at these sites is similar to placing a bet in a casino, except that your expected return from a casino is usually much better.
The other type is an exchange traded option where the price is determined by the market. Both the buyer and the seller are investors or speculators. With these options you will normally see a much fairer price and an expected return much better than most casino bets. These options are generally longer term options when they are issued. It is also possible for an investor to close a position before the settlement date. These options can be used as part of an intelligent investment strategy, but it is still possible to use them strictly as a betting strategy.
You can get a lot more information on binary options from
http://en.wikipedia.org/wiki/Binary_option