Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

V. Risk and Return 14. Options and Corporate

Finance

(^488) © The McGraw−Hill
Companies, 2002
The Upper Bound What is the most that a call option can sell for? If you think about
it, the answer is obvious. A call option gives you the right to buy a share of stock, so it
can never be worth more than the stock itself. This tells us the upper bound on a call’s
value: A call option will always sell for no more than the underlying asset. So, in our no-
tation, the upper bound is:
C 0 S 0 [14.3]
The Lower Bound What is the least a call option can sell for? The answer here is a lit-
tle less obvious. First of all, the call can’t sell for less than zero, so C 0 0. Furthermore,
if the stock price is greater than the exercise price, the call option is worth at least S 0
E.
To see why, suppose we have a call option selling for $4. The stock price is $10, and
the exercise price is $5. Is there a profit opportunity here? The answer is yes because
you could buy the call for $4 and immediately exercise it by spending an additional $5.
Your total cost of acquiring the stock would be $4  5 $9. If you were to turn around
and immediately sell the stock for $10, you would pocket a $1 certain profit.
Opportunities for riskless profits such as this one are called arbitrages(say “are-bi-
trazh,” with the accent on the first syllable) or arbitrage opportunities.One who arbi-
trages is called an arbitrageur,or just “arb” for short. The root for the term arbitrageis
the same as the root for the word arbitrate,and an arbitrageur essentially arbitrates
prices. In a well-organized market, significant arbitrages will, of course, be rare.
In the case of a call option, to prevent arbitrage, the value of the call today must be
greater than the stock price less the exercise price:
C 0 S 0
E
460 PART FIVE Risk and Return

FIGURE 14.1

Value of a Call Option at

Expiration for Different

Stock Prices

Call option value

at expiration

(C 1 )

Stock price

at expiration

Exercise price (S 1 )

(E)

S 1  E

45 o

S 1  E

As shown, the value of a call option at expiration is equal to zero if the

stock price is less than or equal to the exercise price. The value of the call

is equal to the stock price minus the exercise price (S 1 – E) if the stock

price exceeds the exercise price. The resulting "hockey stick" shape is

highlighted.