A PUT OR PUT OPTION
    A put or put option is a contract between two parties to exchange an asset (the underlying), at a specified price (the strike), by a predetermined date (the expiry or maturity). One party, the buyer of the put, has the right, but not an obligation, to re-sell the asset at the strike price by the future date, while the other party, the seller of the put, has the obligation to repurchase the asset at the strike price if the buyer exercises the option.
    If the strike is K, and at time t the value of the underlying is S(t), then in an American option the buyer can exercise the put for a payout of K-S(t) up until the option's maturity time T. The put yields a positive return only if the spot price falls below the strike when the option is exercised. A European option can only be exercised at time T rather than any time up until T, and 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 his holdings of the underlying so that if a drastic downward movement of the underling’s price occurs; he has 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.

Instrument models

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 it 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 underling’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.
The put buyer is short on the underlying asset of the put, but long on the put option itself. That is, the buyer wants the value of the put option to increase by a decline in the price of the underlying asset below the strike price. The writer (seller) of a put is long on the underlying asset and short on the put option itself. That is, the seller wants the option to become worthless by an increase in the price of the underlying asset above the strike price. Generally, a put option that is purchased is referred to as a long put and a put option that is sold is referred to as a short put.
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 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 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 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. In order to protect the put buyer from default, the put writer is required to post margin. The put buyer does not need to post margin because the buyer would not exercise the option if it had a negative payoff.                                                                 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 is 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

4 Reasons to Hold Onto an Option 

    When newcomers to the options get started generally, the first thing done is to  learn, and probably memorize, the definition of an option:

A call option is a contract that grants its owner the right, but not the obligation, to buy 100 shares of the underlying asset by paying the strike price per share – for a limited time. Similarly, a put option grants the right to sell.

    An option owner has the right to exercise. If you own an option you are NOT obligated to exercise; it's your choice. As it turns out, there are good reasons not to exercise your rights as an option owner. Selling the option is usually the best choice for an option owner who no longer wants to hold the position.
    An option seller has obligations – which he/she may be called upon to fulfill. The obligation of a call seller is to deliver 100 shares at the strike price, but only if the option owner exercises his/her right before the option expires. The obligation of a put seller is to purchase 100 shares at the strike price, but only if the option owner exercises before the option expires. If called upon to fulfill the conditions of the option contract by its owner, the option seller must honor the contract. In fact, the process is automated and guaranteed. There is no possibility that the contract will not be honored. The seller is informed (in the morning) that last night, when the markets were closed, the transaction occurred. Thus, stock disappears from the account of the call seller and is replaced with the proper amount of cash; or stock appears in the account of the put seller, and the cash to buy those shares is removed.
          When is it wrong to exercise?
This discussion is easier to follow when we use an example. Let's take the following as given:

• LEKINJOY is currently trading at $99.00
• You own one LEKINJOY Oct 90 call option
• The LEKINJOY Oct 90 call option is priced at $9.50
• October expiration arrives in two weeks

1. Increased Risk
   Exercising this call option prior to expiration increases risk. But to make it even worse, you have nothing to gain for taking on that added risk.
   When you own the call option, the most you can lose - from today, it does not matter what price you paid to buy this option earlier - is the value of the option, or $950. If the stock rallies, you still own the right to pay $90 per share for JKLM. It is not necessary to own the shares to profit from a price increase. You lose nothing by continuing to hold the call option. If you decide you must own the shares (instead of the call option) and exercise, you effectively sell your option at zero (because it has been used) and buy stock at $90 per share. Let's assume that one week passes and the company makes an unexpected announcement. The market does not like the news and the stock opens for trading at $85 and soon sinks to $83. That's unfortunate. If you own the call option, it has become almost worthless. Your account is worth $950 less than it was just one week ago.
       But, if you exercised your option and own stock, your account value has decreased by $1,600, or the difference between $9,900 and $8,300. This is an unacceptable loss. There was never any chance to gain by exercising the call option, and although you were unlucky, you lost an additional $650 by exercising. Yes, by exercising. If you still owned the option, you would have fared better.
   To clarify any misconceptions: If you wanted to take your profit, you could have sold your option earlier. The decision 'not to exercise' did NOT force you to hold onto the option and then incur a loss. It's important to understand that most people who exercise a call option do not want to invest in the stock. Instead, they exercise and then sell the shares. There is no need to do that. Just sell the option instead.
2. Extra Commissions
   when you sell the option, you pay a commission. When you exercise an option, you (with most brokers) pay a fee to exercise. Then you pay another commission to sell the shares. This combination probably costs more (be certain you understand your broker's fee and commission schedule) than simply selling the call. There is no need to give your broker a bonus when there is nothing in it for you.
3. Extra Interest Costs
   when you buy an option, you pay for it. There are no additional costs to hold the position. When you convert that option into stock by exercising, you now own the shares. You must use cash – which will no longer be earning interest – or borrow cash from your broker – and pay interest on that loan. In either case, you are accruing interest charges, with no offsetting gains. There is no benefit to be derived by owning stock. Just hold (or sell) the call option and don't pay additional expenses.
4. Trading on Margin
   If you trade on margin, the requirement is greater when you own stock as compared with owning call options. This may not be true for low-priced stocks.        Two Exceptions
   occasionally the stock pays a big dividend and exercising a call option to capture that dividend may be worthwhile.
   If you own an option that is deep in the money, you may not be able to sell it at its fair value. If the bids are too low, it's preferable to exercise the option then immediately unload the stock position. This is not a common occurrence.
   
   Conclusion
   There are solid reasons for not exercising an option before expiration arrives. Each of those reasons also applies at expiration. Unless you want to own a position in the underlying stock, it is almost always wrong to exercise an option when you can sell it instead.