THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 396
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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
*
0
X
*
X
Asset price at
expiration (S )
*
Profit line
from writing
a put option
F I G U R E 14 - 2
Profits from Buying and Writing a Put Option
