A call option is a financial contract between two parties, the buyer and the seller of the option. The buyer of the option has the right but not the obligation to buy an agreed quantity of a particular commodity or financial instrument (the underlying instrument) from the seller of the option at a certain time for a certain price (the strike price). The seller assumes the corresponding obligations.

"Selling" in this context is not the supplying of a physical or financial asset (the underlying instrument), rather it is the granting of the right to buy the underlying, against a fee - the option price or premium.

Exact specifications may differ depending on option style. A european call option allows the holder to exercise, i.e. to buy, on the delivery date only. An american call option allows exercise at any time during the life of the option.

The stock option, the option to buy stock in a particular company, is the most widely-known call. However options are traded on many other financial instruments - such as interest rates (see interest rate cap) - as well as on physical assets such as gold or crude oil.

Example of a call option on a stock

I buy a call on Microsoft Corp. strike price $50, exercise June 1 2005.

• If the share price is actually $60 on that day (the spot price) 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 minus the fee I paid for the option.
• 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). The option would expire worthless.
• Thus, in any future state of the world, I am certain not to lose money on the underlying by owning the option; my loss is limited to the fee I have paid.

From the above, it is clear that a call option has positive monetary value when the underlying instrument has a spot price (S) above the strike price (K). Since the option will not be exercised unless it is "in-the-money".

Prior to exercise, the option value, and therefore price, varies with the underlying price and with time. The call price must reflect the "likelihood" or chance of the option "finishing in-the-money". The price should thus be higher with more time to expiry, and with a more volatile underlying instrument. 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 formula used, the buyer and seller must agree this value initially.