Editing Put option (section)

=== Writing a put ===
The writer receives a premium from the buyer. If the buyer exercises their option, the writer will buy the stock at the strike price. If the buyer does not exercise their 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 $50 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 (finance)|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 (finance)|volatility]] of the underlying, and increase of interest rates. [[Valuation of options|Option pricing]] is a central problem of [[financial mathematics]].