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CHAPTER 21
OPTIONS VALUATION
21.1 OPTION VALUATION: INTRODUCTION
In the previous chapter, we examined option markets and strategies. We ended
by noting that many securities contain embedded
options
that affect both their
values and their riskreturn characteristics. In this chapter, we turn our attention
to optionvaluation issues. To understand most optionvaluation models
requires
considerable mathematical and statistical background. Still, many of
the ideas and insights of these models can be demonstrated in simple examples,
and we will concentrate on these.
1. Intrinsic and Time Values
Consider a call option that is outofthemoney at the moment, with the stock
price below the exercise price. This does not mean the option is
valueless
. Even
though immediate exercise today would be unprofitable, the call retains a
positive value because there is always a chance the stock price will increase
sufficiently by the expiration date to allow for profitable exercise. If not, the
worst that can happen is that the option will expire with zero value.
The value
S
0
— X
is sometimes called the
intrinsic value
of an inthemoney
call options because it gives the payoff that could be obtained by immediate
exercise. Intrinsic value is set equal to zero
for outofthemoney or atthe
money options. The difference between the actual call price and the intrinsic
value is commonly called the
time value
of the option. (Time value in the options
context refers simply to the
deference
between the option’s price and the value the option
would have if it were expiring immediately. It is the part of the option’s value that may be
attributed to the fact that it sill has positive time expiration
.)
Most of an option’s time value typically is a type of "
volatility value
." Because
the option holder can choose not to exercise, the payoff cannot be worse than
zero. Even if a call option is out of the money now, it still will sell for a positive
price because it offers the
potential
for a profit if the stock price increases, while
imposing no risk of additional loss should the stock price fall. The volatility
value lies in the right
not
to exercise the call if that action would be
unprofitable. The option to exercise as oppose to the obligation to exercise,
provides insurance against poor stock price performance.
As the stock price increases substantially, it becomes more likely that the call
option will be exercised by expiration. Ultimately, with exercise all but assured,
the volatility value becomes
minimal
. As the stock price gets ever larger, the
1
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View Full Document option value approaches the "
adjusted
"
intrinsic
value, that is, the stock price
minus
the present value of the exercise price,
S
0

PV
(X).
This discussion
presumes the stock pays no dividends until after option expiration. (If the stock
does pay dividends, the adjusted intrinsic value of the option must subtract the value of the
dividends (D) the stock will pay out before the call is exercised. Adjusted intrinsic value
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This note was uploaded on 09/25/2011 for the course FINA 4320 taught by Professor John during the Spring '11 term at Houston Baptist.
 Spring '11
 john

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