364 PA R T I V The Management of Financial Institutions expected to fall As with calls, the buyer of a put is said to be long in a put and the writer of a put is said to be short in a put Also, as with calls, the buyer of a put option will have to pay a premium, called a put premium, in order to get the writer to sign the contract and assume the risk The solid line in Figure 14-2 illustrates the profit line from buying a put with an exercise price of X and a premium of At a price of X or higher, the put will not be exercised, resulting in a loss of the premium At a price below X , the put is sufficiently deep in the money to cover the option premium and yield a net profit In fact, between X and X, the put will be exercised, but the gain is insufficient to cover the cost of the premium The payoff function from writing a put is the mirror image of that from buying a put and is represented by the dashed line in Figure 14-2 As with writing a call, the writer of a put receives the put premium up front and must sell the asset underlying the option if the buyer of the put exercises the option to sell In general, the value of a put option P at the expiration date with exercise price X and asset price S (at that time) is P max (X S, 0) That is, the value of a put at maturity is the difference between the exercise price S, or zero, of the option and the price of the asset underlying the option, X whichever is greater If the stock price happens to be greater than the exercise price (S > X ), the put is said to be out of the money and will expire worthless If the asset price happens to be less than the exercise price (S X ), the put is said to be in the money and the owner will exercise it for a net profit of P If S X, the put is said to be at the money Remembering which is a call option and which is a put option is not always easy To keep them straight, just remember that having a call option to buy an asset is the same as having the option to call in the asset for delivery at a specified price Having a put option to sell an asset is the same as having the option to put up an asset for the other party to buy Net Profit Profit line from buying a put option * X * X Asset price at expiration (S ) * Profit line from writing a put option F I G U R E 14 - Profits from Buying and Writing a Put Option