Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

VIII. Topics in Corporate

Finance

24. Option Valuation © The McGraw−Hill^847
    Companies, 2002

Recall from our earlier chapter on options that the intrinsic value of an option is:

Call intrinsic value Max[S
E, 0]

Put intrinsic value Max[E
S, 0]

where “Max[S
E, 0]” just means S
Eor 0, whichever is bigger. American-style op-

tions can never sell for less than their intrinsic value because, if one did, there would be

an arbitrage opportunity. For example, suppose a stock sells for $60. A three-month call

option with a $50 strike price sells for $8. What do you think?

You think you are going to be rich because you can buy the option for $8, exercise it

for $50, then sell the stock for $60 for a $2 riskless profit. To prevent this type of sim-

ple arbitrage, the option has to sell for at least its intrinsic value of $60 
 50 $10. In

reality, the option might sell for $11. The extra $1 in value over the intrinsic value is

called the “time premium.” In other words, an option’s value can be written as:

Option value Intrinsic value Time premium

It is the time premium that wastes away or decays as time goes by. The reason is that the

day an option expires, it is worth exactly its intrinsic value because, on that day, it must

be exercised or torn up. The existence of the time premium also explains our earlier ob-

servation that a call option is always worth more alive than dead. If you exercise an op-

tion, you receive the intrinsic value. If you sell it, you get the intrinsic value plus any

remaining time premium.

822 PART EIGHT Topics in Corporate Finance

FIGURE 24.2

0 3 6 9 12 15 18 21 24 27 30 33 36 39 42

Put Price

Call Price

45 48 51 54 57 60

35

30

25

20

15

10

5

0

Time to Expiration (months)

Option Price ($)

Input values:

S= $100

E= $100

R= 5%

= 25%

Option Prices and Time to Expiration

Time Premiums

At the end of September 2001, shares in Microsoft were going for about $51.20. A call option

expiring in January of 2002 with a $55 strike was quoted at $3.70. A put with the same strike

was quoted at $7.90. For both options, what are the intrinsic value and time premium?

EXAMPLE 24.7

Slide 24.22Figure 24.2