# Put Option

A put or put option is a deal between two parties to exchange an underlying instrument, at a predetermined price (the strike), by a specified date (also referred to as a maturity date).

While one party, the buyer of the put, has the right, but no obligation, to sell the underlying instrument at the strike price by the future date, the other party, the seller of the put, has the obligation to purchase the asset at the strike price should the buyer exercises the option.

If the strike is denoted by K and T stands for the maturity time, now, the buyer exercises the put at a time t, the buyer can anticipate to receive a payout of K-S (t), if the price of the underlying S(t) at that time is lower than K.

The option deal must occur by time T; as the time of the execution is clearly specified by the type of put option. In the United States, an option can be exercised at any time before or equal to T; while in European option it can be exercised only at time T.

A Bermudan option can be exercised only on those dates which are listed in the terms of the contract. Should the option is not exercised by maturity, it expires valueless. (Remember that the buyer will not exercise the option on specified 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 protect their holdings of the underlying asset so that if a significant downward movement of the underlying instrument’s price happens, they have the option to sell the holdings at the strike price. Put option’s another use is for speculation: an investor can take a short position in the underlying instrument without getting directly involved trading.

Puts may also be combined with some other derivatives as part of more intricate investment strategies (also referred to as financial engineering) , and in particular, may be useful for hedging.

With the help of put-call parity, a European put can be changed by buying the appropriate call option and selling an appropriate forward contract.

Instrument Models

The terms for exercising the option’s right to sell – varies, depending upon the option style. A European put option lets the holder to exercise the put option for a short period of time right before the date of maturity, while an American put option gives right to exercise at any time before expiration.

The most extensively-traded put options are on equities; however they are traded on many other instruments such as interest rates or commodities.

The put buyer either hopes that the underlying instrument’s price will drop by the exercise date or anticipates protecting a long position in it. The benefit of buying a put over short selling the asset is that the option owner’s risk of loss is restricted to the premium paid for it, whereas the asset short seller’s risk of loss can stretch to any extent (its price can increase greatly, in fact, in theory it can rise substantially, and such a rise is the short seller’s loss). The put buyer’s hope (risk) of gain is limited to the option’s strike price minus the underlying instrument’s spot price and the premium/fee paid for it.

The put writer expects that the underlying security’s price will increase, not lessen. The writer sells the put to obtain the premium. The put writer’s entire potential loss is restricted to the put’s strike price minus the spot and premium previously received. Puts can be also exercised to minimize the writer’s portfolio risk and may be part of an option spread.

The put buyer is short on the underlying asset of the put, but at the same time long on the put option itself. To be exact, the buyer hopes the value of the put option to rise by a fall in the price of the underlying asset below the strike price. The writer (seller) of a put is long on the underlying asset but short on the put option itself. To be precise, the seller anticipates the option to become valueless by a rise in the price of the underlying asset above the strike price. By and large, a put option that is purchased is called as a long put and a put option that is sold is called as a short put.

A naked put, also referred to as uncovered put, is a put option whose writer (the seller) does not have a position in the underlying security or any other instrument. This strategy is best employed by investors who hope to accumulate a position in the underlying stock, but as long as the price is low enough. If the buyer is not able to exercise the options, then the writer keeps the option premium as a “gift” for playing the game.

If the underlying stock’s market price is under the option’s strike price when expiration nears, the option owner (buyer) can exercise the put option, prompting the writer to buy the underlying stock at the strike price. This lets the exerciser (buyer) to obtain gains from the difference between the stock’s market price and the option’s strike price.

But if the stock’s market price is over the option’s strike price at the end of maturity day, the option expires valueless, and the owner’s loss is restricted to the premium (fee) paid for it (the writer’s profit).

The seller’s potential loss on a naked put can be considerable. If the stock drops all the way to zero (bankruptcy), his loss is equal to the strike price (at which he should buy the stock to cover the option) less the premium received. The potential advantage is the premium obtained when selling the option: if the stock price is over the strike price at expiration, the option seller holds the premium, and the option expires valueless. During the option’s life span, if the stock falls down, the option’s premium may rise (depending on how far the losses stretch (stock’s price) and how much time passes.

If it does, it turn out be more expensive to close the position (repurchase the put, sold earlier), resulting in a loss. If the stock price totally cave in before the put position is closed, the put writer potentially can face massive loss. In order to shield the put buyer from default, the put writer is obliged to post margin. The put buyer does not require posting margin because the buyer would not use the option if it had a negative payoff.

Example of put option on stock

A buyer hopes the price of a stock will decline. He pays a premium which he will on no account get back, except it is sold before it expires. The buyer has the right to sell the stock at the strike price.

Writing a put

The writer will get a premium from the buyer. If the buyer exercises his option, the writer will purchase the stock at the strike price. If the buyer fails to exercise his option, the writer’s profit is the premium.

- “Trader A” (Put Buyer) buys a put contract to sell 100 shares of PQR Corp. to “Trader B” (Put Writer) for $50 per share. The existing price is $55 per share, and Trader A pays a premium of $5 per share. If the price of PQR stock drops to $40 a share right before expiration, then Trader A can exercise the put by purchasing 100 shares for $4,000 from the stock market, then selling them to Trader B for $5,000.

Trader A’s entire earnings (S) can be calculated at $500. The sale of the 100 shares of stock at a strike price of $50 to Trader B will amount to $5,000(P). The buying of 100 shares of stock at $40 = $4,000 (Q). The put option premium paid to trader B for purchasing the contract of 100 shares at $5 per share, not including commissions = $500 (R). Thus S = ( P – Q ) – R = ($5,000 – $4,000 ) – $500 = $500.

- If, on the other hand, the share price remains intact, that is, does not fall below the strike price (in this case, $50), then Trader A would not exercise the option (since selling a stock to Trader B at $50 would cost Trader A more than that to buy it). Trader A’s option would be valueless and he would have lost the entire investment, the fee (premium) for the option contract, $500 ($5 per share, 100 shares per contract). Trader A’s total loss is restricted to the cost of the put premium in addition to the sales commission for buying it.

A put option is said to have inherent value when the underlying instrument has a spot price (S) under the option’s strike price (K). Upon exercise, a put option is estimated at K-S if it is “in-the-money”, or else its value is zero. Before exercising, an option has time value apart from its intrinsic value. The following factors lessen the time value of a put option: shortening of the time to expire, decline in the volatility of the underlying instrument, and an increase of interest rates.