Introduction to Corporate Finance

Ross et al.: Fundamentals

of Corporate Finance, Sixth

Edition, Alternate Edition

VIII. Topics in Corporate

Finance

(^848) 24. Option Valuation © The McGraw−Hill
Companies, 2002
Varying the Standard Deviation
Figure 24.3 illustrates the impact on option values of varying the standard deviation of
the return on the underlying asset. As shown, the effect is positive and pronounced for
both puts and calls. In fact, increasing the standard deviation has an almost identical ef-
fect on them.
The sensitivity of an option’s value to the volatility of the underlying asset is called
its vega.^2 Once again, the formula is somewhat complicated, so we will omit it. The
main thing to understand from Figure 24.3 is that option values are very sensitive to
standard deviations, and changes in the volatility of the underlying asset’s return can
have a strong impact on option values.
Varying the Risk-Free Rate
We illustrate the effect of changing the risk-free rate on option values in Figure 24.4. As
shown, increasing the risk-free rate has a positive impact on call values and a negative
impact on put values. Notice, however, that for realistic changes in interest rates, option
values don’t change a lot. In other words, option values are not as sensitive to changes
CHAPTER 24 Option Valuation 823
Beginning with the call option, we see that it is out of the money because the $55 strike
price is higher than the $51.20 stock price. The intrinsic value is zero, and the entire $3.70 is
therefore time premium. The put is in the money, and its intrinsic value is $55
51.20 
$3.80. The put’s value is $7.90, so the time premium is $7.90
3.80 $4.10.

FIGURE 24.3

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70

Put Price

Call Price

75 80 85 90 95 100

25

20

15

10

5

0

Sigma (%)

Option Price ($)

Input values:

S= $100

E= $100

t= 3 months

R= 5%

Option Prices and Sigma

vega

Measures the sensitivity

of an option’s value to a

change in the standard

deviation of the return on

the underlying asset.

(^2) The Greek scholars among you will recognize that “vega” is not a Greek letter. (It is a star in the
constellation Lyra and also a particularly forgettable automobile manufactured by Chevrolet in the 1960s
and 1970s.)
Slide 24.25Figure 24.3