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^837
    Companies, 2002

If we assume that Ris the continuously compounded risk-free rate per year, then we

could write this as:

SPEe
RtC [24.4]

where tis the time to maturity (in years) on the options.

Finally, suppose we are given an EAR and we need to convert it to a continuously

compounded rate. For example, if the risk-free rate is 8 percent per year compounded

annually, what’s the continuously compounded risk-free rate?

Going back to our first formula, we had that:

EAR eq
 1

Now, we need to solve for q, the continuously compounded rate. Plugging in the num-

bers, we have:

.08 eq
 1

eq1.08

We need to take the natural logarithm (ln) of both sides to solve for q:

ln(eq) ln(1.08)

q.07696

or about 7.7 percent. Notice that most calculators have a button labeled “ln,” so doing

this calculation involves entering 1.08 and then pressing this key.

CONCEPT QUESTIONS

24.1a What is a protective put strategy?

24.1bWhat strategy exactly duplicates a protective put?

812 PART EIGHT Topics in Corporate Finance

Even More Parity

Suppose a share of stock sells for $30. A three-month call option with a $25 strike sells for

$7. A three-month put with the same maturity sells for $1. What’s the continuously com-

pounded risk-free rate?

We need to plug the relevant numbers into the PCP condition:

SPEe
RtC

$30  1 $25 e
R(1/4) 7

Notice that we used one-fourth for the number of years because three months is a quarter of

a year. We now need to solve for R:

$24 $25 e
R(1/4)

.96 e
R(1/4)

ln(.96) ln(e
R(1/4))


.0408 
R(1/4)

R.1632

or about 16.32 percent, which would be a very high risk-free rate!

EXAMPLE 24.4