A European style call (put) option is a security giving the holder the right, but not the obligation, to buy (sell) a pre-specified quantity of the underlying asset, at a pre-specified price (the exercise or strike price), on a pre-specified date (the maturity or expiration date). American-style options confer the same privileges to the holder as the European option, but also provide the owner with the right to exercise the option on or after the exercise date. If an option is not exercised on or before the expiration date, then it expires worthless.

Although options (also called contingent claims or derivative instruments) have been traded for centuries, it was only in April 1973 that the first organized market for trading options opened to trade call options on sixteen common stocks. The initial success of the Chicago Board Options Exchange (CBOE) prompted a rapid increase in the number of stocks with listed options and also in exchanges offering them. During the 1980s this was followed by an expansion in markets to include options on fixed-income securities, currencies and a variety of stock and bond indices, as well as a number of commodities. Although these instruments remain relatively specialized, the theory behind their pricing extends across the whole area of financial economic theory, owing to the fact that option-like structures appear in virtually every part of this vast field. The theory has been used to value shares of a firm, business decisions, risky debt, deposit and pension fund insurance, and wage bargaining as well as currency fluctuations.