Investments, tenth edition

   Restrictions on the Value of a Call Option 

 The most obvious restriction on the value of a call option is that its value cannot be nega-

tive. Because the option need not be exercised, it cannot impose any liability on its holder; 

moreover, as long as there is any possibility that at some point the option can be exercised 

profitably, it will command a positive price. Its payoff is zero at worst, and possibly posi-

tive, so it has some positive value. 

 We can place another lower bound on the value of a call option. Suppose that the stock 

will pay a dividend of  D  dollars just before the expiration date of the option, denoted by 

 T  (where today is time 0). Now compare two portfolios, one consisting of a call option on 

one share of stock and the other a leveraged equity position consisting of that share and 

borrowing of ( X   1   D )/(1  1   r  

 f 

 ) 

 T 

  dollars. The loan repayment is  X   1   D  dollars, due on the 

expiration date of the option. For example, for a half-year maturity option with exercise 

price $70, dividends to be paid of $5, and effective annual interest of 10%, you would pur-

chase one share of stock and borrow $75/(1.10) 

1/2

   5  $71.51. In 6 months, when the loan 

matures, the payment due is $75. 

 At that time, the payoff to the leveraged equity position would be