Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

VIII. Topics in Corporate

Finance

(^840) 24. Option Valuation © The McGraw−Hill
Companies, 2002
R4% per year, continuously compounded
60% per year
t3 months
With these numbers, d 1 is:
d 1 [ln(S/E) (R^2 /2) t]/( )
[ln(70/80) (.04 .6^2 /2) ^1  4 ]/(.6  )

.26
d 2 d 1


.26
.6 

.56
Referring to Table 24.3, the values of N(d 1 ) and N(d 2 ) are .3974 and .2877, respectively.
Plugging all the numbers in:
CSN(d 1 )
Ee
RtN(d 2 )
$70 .3974
$80 e
.04(1/4).2877
$5.03
If you take a look at the Black-Scholes formula and our examples, you will see that
the price of a call option depends on five, and only five, factors. These are the same fac-
tors that we identified earlier: namely, the stock price, the strike price, the time to matu-
rity, the risk-free rate, and the standard deviation of the return on the stock.
^1  4
t
^1  4
t
CHAPTER 24 Option Valuation 815
Call Option Pricing
Suppose you are given the following:
S$40
E$36
R4% per year, continuously compounded
70% per year
t3 months
What’s the value of a call option on the stock?
We need to use the Black-Scholes OPM. So, we first need to calculate d 1 and d 2 :
d 1 [ln(S/E) (R^2 /2) t]/( )
[ln(40/36) (.04 .7^2 /2) ^1 ^4 ]/(.7  )
.50
d 2 d 1

.50
.7 
.15
Referring to Table 24.3, the values of N(d 1 ) and N(d 2 ) are .6915 and .5597, respectively. To get
the second of these, we averaged the two numbers on each side, (.5557 .5636)/2 .5597.
Plugging all the numbers in:
CSN(d 1 )
Ee
RtN(d 2 )
$40 .6915
$36 e
.04(1/4).5597
$7.71

^1  4

t

^1  4

t

EXAMPLE 24.5