Put option: Wikis


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A put option (sometimes simply called a "put") is a financial contract between two parties, the seller (writer) and the buyer of the option. The buyer acquires a short position with the right, but not the obligation, to sell the underlying instrument at an agreed-upon price (the strike price). If the buyer exercises his right to sell the option, the seller is obliged to buy it at the strike price. In exchange for having this option, the buyer pays the writer a fee (the option premium). The terms for exercising the option's right to sell it differ depending on option style. A European put option allows the holder to exercise the put option for a short period of time right before expiration, while an American put option allows exercise at any time before expiration.

The most widely-traded put options are on equities, but they are traded on many other instruments such as interest rates (see interest rate floor) or commodities.

The put buyer either believes that the underlying asset's price will fall by the exercise date or hopes to protect a long position in it. The advantage of buying a put over short selling the asset is that the option owner's risk of loss is limited to the premium paid for it, whereas the asset short seller's risk of loss is unlimited (its price can rise greatly, in fact, in theory in can rise infinitely, and such a rise is the short seller's loss.) The put buyer's prospect (risk) of gain is limited to the option's strike price less the underlying's spot price and the premium/fee paid for it.

The put writer believes that the underlying security's price will rise, not fall. The writer sells the put to collect the premium. The put writer's total potential loss is limited to the put's strike price less the spot and premium already received. Puts can be used also to limit the writer's portfolio risk and may be part of an option spread.

A naked put, also called an uncovered put, is a put option whose writer (the seller) does not have a position in the underlying stock or other instrument. This strategy is best used by investors who want to accumulate a position in the underlying stock, but only if the price is low enough. If the buyer fails to sell the shares, then the seller keeps the option premium as a 'gift' for playing the game.

If the underlying stock's market price is below the option's strike price when expiration arrives, the option owner (buyer) can exercise the put option, forcing the writer to buy the underlying stock at the strike price. That allows the exerciser (buyer) to profit from the difference between the stock's market price and the option's strike price. But if the stock's market price is above the option's strike price at the end of expiration day, the option expires worthless, and the owner's loss is limited to the premium (fee) paid for it (the writer's profit).

The seller's potential loss on a naked put can be substantial. If the stock falls all the way to zero (bankruptcy), his loss is equal to the strike price (at which he must buy the stock to cover the option) minus the premium [(market price)] received. The potential upside is the premium received when selling the option: if the stock price is above the strike price at expiration, the option seller keeps the premium, and the option expires worthless. During the option's lifetime, if the stock moves lower, the option's premium may increase (depending on how far the stock falls and how much time passes). If it does, it becomes more costly to close the position (repurchase the put, sold earlier), resulting in a loss. If the stock price completely collapses before the put position is closed, the put writer potentially can face catastrophic loss.


Example of a put option on a stock

Payoff from buying a put.
Payoff from writing a put.
Buying a Put: 
 A Buyer thinks price of a stock will decrease.
 Pay a premium which buyer will never get back, 
    unless it is sold before expiration.
 The buyer has the right to sell the stock 
    at strike price.
Writing a put:
 Writer receives a premium.
 If buyer exercises the option,  
    writer will buy the stock at strike price. 
 If buyer does not exercise the option, 
    writer's profit is premium.
  • 'Trader A' (Put Buyer) purchases a put contract to sell 100 shares of XYZ Corp. to 'Trader B' (Put Writer) for $50/share. The current price is $55/share, and 'Trader A' pays a premium of $5/share. If the price of XYZ stock falls to $40/share right before expiration, then 'Trader A' can exercise the put by buying 100 shares for $4,000 from the stock market, then selling them to 'Trader B' for $5,000.
Trader A's total earnings (S) can be calculated at $500. 
 Sale of the 100 shares of stock at strike price of $50 
    to 'Trader B' = $5,000 (P)
 Purchase of 100 shares of stock at $40 = $4,000 (Q)
 Put Option premium paid to Trader B for buying the contract of 
    100 shares @ $5/share, excluding commissions = $500 (R)
  • If, however, the share price never drops below the strike price (in this case, $50), then 'Trader A' would not exercise the option. (Why sell a stock to 'Trader B' at $50, if it would cost 'Trader A' more than that to buy it?). Trader A's option would be worthless and he would have lost the whole investment, the fee (premium) for the option contract, $500 (5/share, 100 shares per contract). Trader A's total loss are limited to the cost of the put premium plus the sales commission to buy it.

A put option is said to have intrinsic value when the underlying instrument has a spot price (S) below the option's strike price (K). Upon exercise, a put option is valued at K-S if it is "in-the-money", otherwise its value is zero. Prior to exercise, an option has time value apart from its intrinsic value. The following factors reduce the time value of a put option: shortening of the time to expire, decrease in the volatility of the underlying, and increase of interest rates. Option pricing is a central problem of financial mathematics.

See also


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