Investments, tenth edition

 Option  Valuation 

     21.1 

Option Valuation: Introduction 

   Intrinsic and Time Values 

 Consider a call option that is out of the money 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. 

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 Option 

Valuation 

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 The value  S  

0

   2   X  is sometimes called the    intrinsic  value    of in-the-money call options 

because it gives the payoff that could be obtained by immediate exercise. Intrinsic value is 

set equal to zero for out-of-the-money or at-the-money options. The difference between the 

actual call price and the intrinsic value is commonly called the    time  value    of the option. 

 “Time value” is unfortunate terminology because it may confuse the option’s time value 

with the time value of money. Time value in the options context refers simply to the dif-

ference 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 still 

has positive time to 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 value of the right  not  to exercise 

the call if that action would be unprofitable. The option to exercise, as opposed to the obli-

gation to exercise, provides insurance against poor stock price performance. 

 As the stock price increases substantially, it becomes 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 option value approaches the 

“adjusted” intrinsic value, the stock price minus the present value of the exercise price, 

 S  

0

   2  PV( X ). 

 Why should this be? If you are virtually certain the option will be exercised and the 

stock purchased for  X  dollars, it is as though you own the stock already. The stock cer-

tificate, with a value today of  S  

0

 , might as well be sitting in your safe-deposit box now, 

as it will be there in only a few months. You just haven’t paid for it yet. The present 

value of your obligation is the present value of  X,  so the net value of the call option is 

 S  

0

   2  PV( X ).  

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  Figure  21.1  illustrates the call option valuation function. The value curve shows that 

when the stock price is very low, the option is nearly worthless, because there is almost 

no chance that it will be exercised. When the stock price is very high, the option value 

approaches adjusted intrinsic value. In the midrange case, where the option is approxi-

mately at the money, the option curve diverges from the straight lines corresponding to 

adjusted intrinsic value. This is because although exercise today would have a negligible 

(or negative) payoff, the volatility value of the option is quite high in this region. 

  The call always increases in value with the stock price. The slope is greatest, however, 

when the option is deep in the money. In this case, exercise is all but assured, and the 

option increases in price one-for-one with the stock price.