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^835
    Companies, 2002

SPV(E) C
P [24.3]

$40/1.005^3  4
3

$40.41

The PCP condition really says that between a riskless asset (like a T-bill), a call option,

a put option, and a share of stock, we can always figure out the price of any one of the

four given the prices of the other three.

Continuous Compounding: A Refresher Course

Back in Chapter 6, we saw that the effective annual interest rate (EAR) on an investment

depends on compounding frequency. We also saw that, in the extreme, compounding

can occur every instant, or continuously. So, as a quick refresher, suppose you invest

$100 at a rate of 6 percent per year compounded continuously. How much will you have

in one year? How about in two years?

In Chapter 6, we saw that the EAR with continuous compounding is:

EAR eq
 1

where qis the quoted rate (6 percent, or .06, in this case) and eis the number

2.71828..., the base of the natural logarithms. Plugging in the numbers, we get:

EAR eq
 1

2.71828.06
 1

.06184

810 PART EIGHT Topics in Corporate Finance

Put-Call Parity

Suppose a share of stock sells for $60. A six-month call option with a $70 strike price sells for

$2. The risk-free rate is .4 percent per month. What’s the price of a six-month put option with

a $70 strike?

If we just use the PCP condition to solve for the put price, we get:

P PV(E) C
S

$70/1.004^6  2 
$60

$10.34

Notice that, in this example, the put option is worth a lot more than the call. Why?

EXAMPLE 24.1

More Parity

Suppose a share of stock sells for $110. A one-year, at-the-money call option sells for $15. An

at-the-money put with the same maturity sells for $5. Can you create a risk-free investment

by combining these three instruments? How? What’s the risk-free rate?

Here, we can use the PCP condition to solve for the present value of the strike price:

PV(E)SP
C

$110  5 
 15

$100

The present value of the strike price is thus $100. Notice that because the options are at the

money, the strike is the same as the stock price, $110. So, if you put $100 in a riskless invest-

ment today and receive $110 in one year, the implied risk-free rate is obviously 10 percent.

EXAMPLE 24.2