Introduction to Corporate Finance

8: Options

1 Explain the difference between the share price, the exercise price and the option premium.

Which of these are market prices determined by the forces of supply and demand?

2 Explain the difference between a long position and a short position. With respect to call options,

what is the maximum gain and loss possible for an investor who holds the long position? What is

the maximum gain and loss for the investor on the short side of the transaction?

3 Suppose an investor holds a call option on shares in Woolworths and decides to exercise the

option. What will happen to the total shares of ordinary shares outstanding for Woolworths?

4 Which of the following would increase the value of a put option – an increase in the share price or

an increase in the strike price?

CONCEPT REVIEW QUESTIONS 8-1

8-2 OPTION PaYOFF dIaGraMS

So far, our discussion of options has been mostly descriptive. Now we turn to the problem of determining

an option’s market price. Valuing an option is an extraordinarily difficult problem – so difficult, in fact,

that the economists who solved the problem won a Nobel Prize for their efforts. In earlier chapters, when

we studied the pricing of shares and bonds, we began by describing their cash flows. We do the same

here, focusing initially on the relatively simple problem of outlining options’ cash flows on the expiration

date. Eventually, that will help us understand the intuition behind complex option pricing models.

8-2a Call OPTION PaYOFFS

We define an option’s payoff as the price an investor would be willing to pay for the option the instant

before it expires.^6 An option’s payoff is distinct from its price, or premium, because the payoff only refers

to the price of the option at a particular instant in time, the expiration date. Graphs that illustrate an

option’s payoff as a function of the underlying share price are called payoff diagrams. Payoff diagrams are

extremely useful tools for understanding how options behave and how they can be combined to form

portfolios with fascinating properties.

Suppose an investor purchases a call option with a strike price of $75 and an expiration date three months

in the future. To acquire this option, the investor pays a premium of $8. When the option expires, what will it

be worth? If the underlying share price is less than $75 on the expiration date, the option will be worthless. No

one would pay anything for the right to buy this share for $75 when they can easily buy it for less in the market.

What if the share price equals $76 on the expiration date? In that case, owning the right to buy the share

at $75 is worth $1, the difference between the share’s market price and the option’s exercise price. Ignoring

transactions costs, an investor who owns the option can buy the share for $75 and immediately sell it in the

market for $76, earning a $1 payoff. In general, the payoff of this option will equal the greater of:

■ $0, if the share price is less than $75 at expiration; or

■ the difference between the share price and $75, if the share price is more than $75 at expiration.

6 Alternatively, we could define the payoff as the value an investor would receive, ignoring transactions costs, if he or she exercised the option

when it expired. If it did not make sense to exercise the option when it expired, the payoff would be zero.

LO8.2

payoff

The value received from

exercising an option on the

expiration date (or zero),

ignoring the initial premium

required to purchase the

option

payoff diagrams

A diagram that shows how the

expiration date payoff from

an option or a portfolio varies,

as the underlying asset price

changes