A put or put option is a contract between two parties to exchange an asset, the underlying, for a specified amount of cash, the strike, by a predetermined future date, the expiry or maturity. One party, the buyer of the put, has the right, but not an obligation, to sell the asset at the strike price by the future date, while the other party, the seller, has the obligation to buy the asset at the strike price if the buyer exercises the option.
If the strike is K and maturity time is T, if the buyer exercises the put at a time t, the buyer can expect to receive a payout of K-S(t), if the price of the underlying S(t) at that time is less than K. The exercise t must occur by time T; precisely what exact times are allowed is specified by the type of put option. An American option can be exercised at any time before or equal to T; a European option can be exercised only at time T; a Bermudan option can be exercised only on specific dates listed in the terms of the contract. If the option is not exercised by maturity, it expires worthless. (Note that the buyer will not exercise the option at an allowable date if the price of the underlying is greater than K.)
The most obvious use of a put is as a type of insurance. In the protective put strategy, the investor buys enough puts to cover their holdings of the underlying so that if a drastic downward movement of the underlying’s price occurs, they have the option to sell the holdings at the strike price. Another use is for speculation: an investor can take a short position in the underlying without trading in it directly.
Puts may also be combined with other derivatives as part of more complex investment strategies, and in particular, may be useful for hedging. Note that by put-call parity, a European put can be replaced by buying the appropriate call option and selling an appropriate forward contract.
Example of a put option on a stock
- Buying a put
A Buyer thinks the price of a stock will decrease. He pays a premium which he will never get back, unless it is sold before it expires. The buyer has the right to sell the stock at the strike price.
- Writing a put
The writer receives a premium from the buyer. If the buyer exercises his option, the writer will buy the stock at the strike price. If the buyer does not exercise his option, the writer’s profit is the premium.
- "Trader A" (Put Buyer) purchases a put contract to sell 100 shares of XYZ Corp. to "Trader B" (Put Writer) for $50 per share. The current price is $55 per share, and Trader A pays a premium of $5 per share. If the price of XYZ stock falls to $40 a 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. The sale of the 100 shares of stock at a strike price of $50 to Trader B = $5,000 (P). The purchase of 100 shares of stock at $40 = $4,000 (Q). The put option premium paid to trader B for buying the contract of 100 shares at $5 per share, excluding commissions = $500 (R). Thus S = P – (Q+R) = $5,000 – ($4,000+$500) = $500.
- If, however, the share price never drops below the strike price (in this case, $50), then Trader A would not exercise the option (because selling a stock to Trader B at $50 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 per 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.