442 Planning and Forecasting
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, re-
gardless 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 op-
tions. A payoff diagram graphs the payoff of an option as a function of the
underlying asset’s spot price at expiration. Exhibit 13.1 depicts the payoff dia-
gram for the Disney call option with a strike price of $70. 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
or not the option is appropriate for any particular application.
The payoff diagram is f lat and equal to zero in the entire range where the
option is out of the money—that is, where the stock price is less than the strike
price. This means that someone who buys an option might lose his entire in-
vestment in that option. You may pay $3 for the option, and lose 100% of that
$3 by the expiration date. On the brighter side, the payoff diagram confirms
that the most you can lose in an option is the initial premium, the $3 you paid
for it. Unlike, futures or forwards, you will never be called on to make addi-
tional payments at a later date. Initially, you pay for the option, perhaps $3.
From then on you can only receive cash inf lows.
Note that the payoff diagram begins to rise at the point where the stock
price equals the strike price. The payoff is dollar for dollar greater than zero
for every dollar that the stock price exceeds the strike price. Thus we see that
a call option rises in value as the underlying asset rises in price. For this reason,
some people refer to call options as “bullish” instruments.
EXHIBIT 13.1 Call option payoff diagram.
010
5152025300 102030405060708090100Payoff (dollars)Terminal stock price (Strike price = $70)