# Put Option

Put option is an option that gives its holder the right to sell an asset, say bond or stock, at a specified exercise price at the exercise date. Its payoff equals the exercise price minus the price of the underlying asset.

Value of a put option (or simply put) depends on the market price of the underlying asset (the stock, bond, etc.) relative to the exercise price (also called the strike price). Like a call option, but unlike forwards and futures, a put option requires payment of a premium to the writer of the option at the time of the initiation of the option contract.

Investors purchase put option when they believe the stock might fall in value in future. They exercise the option when the market price of the underlying (asset) is lower than the price at which they can put the underlying (asset) to the writer of the option at the exercise price or the strike price. Such option is called in the money option. For example, suppose we own a put option on the stock of Zynga (NASDAQ: ZNGA) with exercise price of $3.19, which we bought a couple months ago. The option is exercisable today and the current price of ZNGA stock is $2.65. We can buy ZNGA stock in the market for $2.65 and put it to the writer at $3.19, earning $0.54 (=$3.19 - $2.65). This $0.54 is the value of the put option. The put option will be worthless if the current stock price is higher than the exercise price of the option, such option is called out-of-the-money option.

A European put option can be exercised only at a specified date i.e. the exercise date while an American put option can be exercised at any time up to the exercise date.

A put option payoff is exactly opposite of an identical call option.

## Payoff Formula

The value of a put option equals the excess of the price at which we can sell the underlying asset to the writer (i.e. the exercise price or the strike price) over the price at which the asset can be sold/purchased in the market.

Like a call option, the value of a put option can never be negative, because it is just an option. When the exercise price is lower than the current market price of the underlying asset, the option holder simply lets the option expire.

Value of a put option can be calculated using the following formula:

Value of Put Option = max(0, exercise price − underlying asset's market price)

## Example

Charlotte Réminiac is a portfolio manager who is not satisfied with Apple Inc.'s current pace of innovation. She believes that Apple's (NYSE: AAPL) share price should drop further in future. She did not want to lock up the money in the stock itself, so she bought 1,000 put options on AAPL stock on 15 June 20X3. The options had an exercise price of $400 per share.

The price fell to $380 by the exercise date. Value the option at the exercise date and tell whether the option should be exercised or not.

Value of a put option = exercise price − market price of the underlying = $400 − $380 = $20 per share

Total value of the options = 1,000 × $20 = $20,000

Charllotte should exercise the options. She can buy 1,000 AAPL shares in the market for $380,000 (=1,000 × $380) and sell them to the option writer for $400,000 (= 1,000 × $400), earning the differential $20,000.