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A call option is an asset that gives the owner the right but not the obligation to buy some other
underlying asset for a set price, on or up to a set date. For example, consider a call option on Disney
stock that gives the owner the right to purchase one share of Disney stock for $30 per share, on or up
to next June 15. (Actually, options are usually sold in blocks covering 100 shares. For expository
purposes, however, we will describe an option on only a single share.) The underlying asset would be
one share of Disney stock. The prespecified price, known as the “strike price,” would be $30 per
share. The expiration date would be June 15. The Disney option might cost $3 initially.
If on the expiration date, June 15, the market price of Disney stock stood at $35, the call option
owner would exercise the option and buy a share of Disney stock for $30. The new share owner could
then turn around and sell the share for $35 in the marketplace, realizing a terminal payoff from the
option of $5. The terminal payoff is $5, so the profit net of the $3 initial option price is $2.
Suppose, alternatively, that the market price of Disney stock on June 15 were $29. It would not be
profitable to exercise the call option and thereby purchase for $30 what is elsewhere available for $29.
In such a case, the option owner would choose not to exercise, and the call would expire worthless. It
is the right not to execute the transaction that is the major difference between options and forwards.
The long party in a forward contract must buy the goods upon expiration whether it is advantageous to
do so or not. By contrast, call option owners do not have to buy the underlying asset if they choose not
to. At expiration, a call option should be exercised if and only if the market price exceeds the strike
price. When the market price is above the strike price, the call option is said to be “in the money.”
When the market price is less than the strike price, the call is “out of the money.” When the market
price equals the strike price, the option is “at the money.” An option that is out of the money, or even
at the money, at expiration will expire unexercised and worthless.
An option‟s payoff is defined as the maximum amount of money the option owner would receive at
expiration, if she totally liquidated her position. If the option expires out of the money, the payoff is
zero. If the option expires in the money, the payoff is the amount of money received from exercising
the call option and then selling the stock in the open market. For example, if the strike price is $30 and
the terminal stock price is $20, the payoff would be zero, since the option would be out of the money
and should not be exercised. If the terminal stock price were $40, the payoff would be $10, since the
option should be exercised, allowing the owner to buy the stock for $30, and then sell that stock for
$40 in the open market. Mathematically, the payoff is the maximum of zero or the stock price minus
the strike price.
The payoff ignores the initial price that was paid for the option. Payoff treats the initial price as a
sunk cost, and measures only what the option owner might subsequently receive. The payoff minus
the initial price is known as the option profit. The option payoff is the same for all owners of the
option, regardless of what they each initially paid for it. Profit, however, depends on what was initially
paid and therefore differs from one investor to another.
A payoff diagram is a valuable analytical device for understanding options. A payoff diagram
graphs the payoff of an option as a function of the underlying asset‟s spot price at expiration. Exhibit
15.1 depicts the payoff diagram for the Disney call option with a strike price of $40. The payoff
diagram is a picture of the option. It tells you when you will receive money and when you will not. It
helps to visualize how the contract will perform, and whether the option is appropriate for any
particular application.