Put option

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Buying a put option - This is a graphical interpretation of the payoffs and profits generated by a put option as seen by the buyer of the option. A lower stock price means a higher profit. Eventually, the price of the underlying security will be low enough to fully compensate for the price of the option.
Writing a put option - This is a graphical interpretation of the payoffs and profits generated by a put option as seen by the writer of the option. Profit is maximized when the price of the underlying security exceeds the strike price, because the option expires worthless and the writer keeps the premium.

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 long position offering the right, but not obligation, to sell the underlying instrument at an agreed-upon price (the strike price). If the buyer exercises the right granted by the option, the writer has the obligation to purchase the underlying at the strike price. In exchange for having this option, the buyer pays the writer a fee (the option premium). The terms for exercise 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 option are on equities. However, options are traded on many other instruments such as interest rates (see interest rate floor) or commodities.

The put buyer either believes it's likely the price of the underlying asset will fall by the exercise date, or hopes to protect a long position in the asset. The advantage of buying a put over short selling the asset is that the risk is limited to the premium. The profit, for a put buyer, is limited to the strike price less the underlying's spot price (in addition to the premium already paid).

The put writer does not believe the price of the underlying security is likely to fall. The writer sells the put to collect the premium. The total loss, for the put writer, is limited to the strike price less the spot and premium already received. Puts can also be used to limit portfolio risk, and may be part of an option spread.

A naked put (also called an uncovered put) is a put option where the option writer (i.e., 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 investor fails to buy the shares, then he keeps the option premium as a 'gift' for playing the game.

If the market price of the underlying stock is below the strike price of the option when expiration arrives, the option owner can exercise the put option and force the writer to buy the underlying stock at the strike price. That allows the exerciser to profit from the difference between the market price of the stock and the option's strike price. But if the market price is above the strike price when expiration day arrives, the option expires worthless and the writer profits by keeping the premium collected when selling the option.

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

[edit] Example of a put option on a stock

Buy 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.
Write 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 expiry, decrease in the volatility of the underlying, and increase of interest rates. Option pricing is a central problem of financial mathematics.

[edit] See also

[edit] Options

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