Investments, tenth edition

  High-Volatility Scenario  

 Stock price 

 $10  

$20  

$30  

$40  

$50 

 Option payoff 

 0  

0  

0  

10  

20 

  Low-Volatility Scenario  

 Stock price 

 $20  

$25  

$30  

$35  

$40 

 Option payoff 

 0  

0  

0  

5  

10 

 If each outcome is equally likely, with probability .2, the expected payoff to the option 

under high-volatility conditions will be $6, but under low-volatility conditions the expected 

payoff is half as much, only $3. 

 Despite the fact that the average stock price in each scenario is $30, the average option 

payoff is greater in the high-volatility scenario. The source of this extra value is the limited 

loss an option holder can suffer, or the volatility value of the call. No matter how far below 

Option Value

Out of the

Money

In the Money

S

0

Time Value

PV(X) X

Value of Call Option

S

0 

– PV(X)

Value of Option

if Now at

Expiration = S – X =

Intrinsic Value

 Figure 21.1 

Call option value before expiration  

bod61671_ch21_722-769.indd   724

bod61671_ch21_722-769.indd   724

7/27/13   1:45 AM

7/27/13   1:45 AM

Final PDF to printer

---

  C H A P T E R  

2 1

 Option 

Valuation

725

$30 the stock price drops, the option holder will get zero. Obviously, extremely poor stock 

price performance is no worse for the call option holder than moderately poor performance. 

 In the case of good stock performance, however, the call will expire in the money, and 

it will be more profitable the higher the stock price. Thus extremely good stock outcomes 

can improve the option payoff without limit, but extremely poor outcomes cannot worsen 

the payoff below zero. This asymmetry means that volatility in the underlying stock price 

increases the expected payoff to the option, thereby enhancing its value.  

2

  

  

 Similarly, longer time to expiration increases the value of a call option. For more distant 

expiration dates, there is more time for unpredictable future events to affect prices, and the 

range of likely stock prices increases. This has an effect similar to that of increased volatil-

ity. Moreover, as time to expiration lengthens, the present value of the exercise price falls, 

thereby benefiting the call option holder and increasing the option value. As a corollary 

to this issue, call option values are higher when interest rates rise (holding the stock price 

constant) because higher interest rates also reduce the present value of the exercise price. 

 

 Finally, the dividend payout policy of the firm affects 

option values. A high-dividend payout policy puts a drag 

on the rate of growth of the stock price. For any expected 

total rate of return on the stock, a higher dividend yield 

must imply a lower expected rate of capital gain. This drag 

on stock price appreciation decreases the potential pay-

off from the call option, thereby lowering the call value. 

 Table 21.1   summarizes  these  relationships.