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text courtesy Wikipedia
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.
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.
