Here in this article I have explained the put option by giving you an example of the put option.

Example of a Put Option on a Stock 

Buy a Put: It is believed by a buyer that price of a stock will decrease. He will pay a premium which he will never get back, unless it is sold before expiration. It is the right of the buyer that he can sell the stock at strike price.

Write a put: A premium is received by a writer. If buyer has decided to exercise the option, then writer will buy the stock at strike price. If the option is not exercised by the buyer, then the writer’s profit is premium. 

Assume that ‘Trader A’ (Put Buyer) purchases a put contract in order to sell 100 shares of XYZ Corp. to ‘Trader B’ (Put Writer) for $50_/share. $55_/share is the current price, and a premium of $5_/share is payed by ‘Trader A’. If right before expiration the price of XYZ stock falls to $40_/share , then ‘Trader A’ is able to exercise the put by buying 100 shares for $4,000 from the stock market, rather then selling them to ‘Trader B’ for $5,000.

• Total earnings (S) of Trader A  can be calculated at $500.
• At strike price of $50, sale of the 100 shares of stock to ‘Trader B’ = $5,000 (P)
• At $40 purchase of 100 shares of stock= $4,000 (Q)
• Put Option premium that has been paid to Trader B for buying the contract of 100 shares @ $5_/share, excluding commissions = $500 (R)
• 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 the option will not be exercised by ‘Trader A’. (Why ‘Trader A’ should sell a stock to ‘Trader B’ at $50, if it would cost ‘Trader A’ more than that to buy it?). So in this case Trader A’s option would be worthless and he would have lost the whole investment that includes the fee (premium) for the option contract, $500 (5_/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.

When the underlying instrument has a spot price (S) below the option’s strike price (K) then a put option is said to have intrinsic value> . Upon exercise, a put option is "in-the-money",  then it is valued at K-S, otherwise its value is zero. An option has time value apart from its intrinsic value, prior to exercise.

Factors that Reduce the Time Value of a Put Option:

Below are the factors that reduce the time value of a put option:

• shortening of the time to expiry,
• decrease in the volatility of the underlying,
• increase of interest rates.

Option pricing has been a central problem of financial mathematics.

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