A call option is a financial contract between two parties, the buyer and the seller of the option, that allows the buyer, then owner, of the option the right but not the obligation to buy an agreed quantity of a particular commodity or financial instrument from the seller of the option at a certain time (or times depending on the exact specification of the contract). for a certain price, known as the strike.
"Selling" in this context is not supplying something that the seller owns, but it means granting the buyer this right, against a fee.
The most widely-known call option is that when the option is to buy stock in a particular company. This is a stock option. However options are traded on many other quantities both financial, such as interest rates (called an interest rate cap) or foreign exchange rates (see foreign exchange option) and physical such as gold or crude oil.
I might enter a contract to have the option to buy a share in Microsoft Corp. on June 1 2005 for $50. If the share price is actually $60 on that day then I would exercise my option (i.e. buy the share from the counter-party). I could then sell it in the open market for $60, i.e. the option would be worth $10; my profit would be $10 . If however the share price is only $40 then I would not exercise the option (if I really wanted to own such a share, I could buy it in the open market for $40, why waste $50 on it). My option would be be worth nothing. Thus in any future state of the world, I am certain not to lose money by owning the option. This implies that the option itself must have some positive value (the price of the option). This value varies with the share price and time. The science of determining this value is the central tenet of financial mathematics. The most common method is to use the Black-Scholes formula. Whatever the method used, the buyer and seller must agree this value initially and the buyer pays the seller this value as a fee.
Like in the case of share trading, buyers and sellers of options do not usually interact directly with each other; the options exchange is intermediary and quotes the market value of the option. The seller has to supply a guarantee to the options exchange that he can fulfill his obligation if the buyer chooses to execute his option.
Example of a call option on a stock
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See also: Derivatives markets, Derivative security, Financial economics, Finance
