Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionVIII. Topics in Corporate
Finance(^842) 24. Option Valuation © The McGraw−Hill
Companies, 2002
R4% per year, continuously compounded
80% per year
t4 months
What’s the value of a putoption on the stock?
For practice, calculate the Black-Scholes call option price and see if you agree that a
call option would be worth about $7.52. Now, recall the PCP condition:
SPEeRtC
which we can rearrange to solve for the put price:
PEeRtCS
Plugging in the relevant numbers, we get:
P$40 e.04(1/3)7.52 40
$6.99
Thus, the value of a put option is $6.99. So, once we know how to value call options, we
also know how to value put options.
A Cautionary Note
For practice, let’s consider another put option value. Suppose we have the following:
S$70
E$90
R8% per year, continuously compounded
20% per year
t12 months
What’s the value of a put option on the stock?
For practice, calculate the call option’s value and see if you get $1.61. Once again,
we use PCP to solve for the put price:
PEeRtCS
The put value we get is:
P$90 e.08(1)1.61 70
$14.69
Is there something about our put option value that seems odd? The answer is yes.
Since the stock price is $70 and the strike price is $90, you could get $20 by exercising
the put immediately, so it looks like we have an arbitrage possibility. Unfortunately, we
don’t. This example illustrates that we have to be careful with assumptions. The Black-
Scholes formula is for European-style options (remember that European-style options
can be exercised only on the final day, whereas American-style options can be exercised
anytime). In fact, our PCP condition is only for European-style options.
What our example shows is that an American-style put option is worth more than a
European-style put. The reason is not hard to understand. Suppose you buy a put with a
strike price of $80. The very best thing that can happen is for the stock price to fall to
zero. If the stock price did fall to zero, no further gain on your option is possible, so you
would want to exercise it immediately rather than wait. If the option is American style,
CHAPTER 24 Option Valuation 817