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Note that the seller of the option undertakes to buy the underlying! In exchange for being granted this option, the buyer pays the seller a fee.

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

The most widely-known put option is the stock option, the option to sell stock in a particular company. However, options are traded on many other assets: financial - such as interest rates (see interest rate floor) - and physical, such as gold or crude oil.

Example of a put option on a stock

• I enter a contract to have the option to sell a share in XYZ Corp. on June 1, 2003, for $50.
• If the XYZ Corp. share price is actually only $40 on that day, then I would exercise my option (i.e. sell the share from the counter-party). I could then buy another share in the open market for $40, 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 more than the option price, say, $60, then I would not exercise the option. If I really wanted to sell such a share, I could do so in the open market for $60, and make more profit than I would by selling through the option. My option would be worthless and I would have lost my whole investment, the fee for the option.
• Thus, in any future state of the world, I am certain not to lose money by owning the option; my loss is limited to the fee I have paid.

This example illustrates that the put option has positive monetary value when the underlying instrument has a spot priceThe spot price of a commodity is the price that is quoted for transaction immeadiately. This is contrasted with a forward price, which is the price at which a commodity may be transacted (bought/sold) at a future date. Stock market. (S) below the strike price (K). Since the option will not be exercised unless it is " in-the-money", the payoff for a put option is

Max[ (K-S) ; 0 ] or formally,

where

Prior to exercise, the option value, and therefore price, varies with the underlying price and with time. The put 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 volatileVolatility is the standard deviation of the change in value of a financial instrument with a specific time horizon. It is often used to quantify the risk of the instrument over that time period. Volatility is typically expressed in annualized terms, and i underlying instrument. The science of determining this value is the central tenet of financial mathematicsFinancial mathematics is the branch of applied mathematics concerned with the financial markets. The subject naturally has a close relationship with the discipline of financial economics, however the subject is narrower in scope and more abstract. A centr. The most common method is to use the Black-ScholesThe Black-Scholes model often simply called Black-Scholes is a model of the varying price over time of financial instruments, and in particular stocks. The Black-Scholes formula is a mathematical formula for the theoretical value of European put and call formula. Whatever the formula used, the buyer and seller must agree this value initially.

Related: MoneynessIn finance, moneyness is a measure of the degree to which a derivative security is likely to have positive monetary value at its expiration. An option is at-the-money if the strike price, i. the price the option holder must pay to exercise the option, is, Option time valueConceptually, the value of an option consists of two components, its intrinsic value and its time value . Time value is simply the difference between option value and intrinsic value. Intrinsic value is the difference between the exercise price of the opt, Call option, Put-call parity

See also: Derivatives markets, Derivative security, Financial economics, Futures, List of finance topics

Options: Stock option, Warrants, Foreign exchange option , Interest rate options, Bond options , Options on futures, Swaption, Interest rate cap, Interest rate floor, Exotic interest rate option, Credit default option, binary option, real option