Investments, tenth edition

     Early Exercise and Dividends 

 

A call option holder who wants to close out 

that position has two choices: exercise the 

call or sell it. If the holder exercises at time  t,  

the call will provide a payoff of  

S  

 t 

      2     X,  

assuming, of course, that the option is in the 

money. We have just seen that the option can 

be sold for at least  S  

 t 

      2   PV( X )   2    PV ( D ). 

Therefore, for an option on a non-dividend-

paying stock,  C  is greater than  S  

 t 

   2   PV ( X ). 

Because the present value of  X  is less than  X  

itself, it follows that 

  C $ S

t

2 PV(X) . S

t

2 X  

 

The implication here is that the pro-

ceeds from a sale of the option (at price  C ) 

must exceed the proceeds from an exercise 

( S  

 t 

      2     X ). It is economically more attractive 

to sell the call, which keeps it alive, than to 

exercise and thereby end the option. In other 

words, calls on  non-dividend-paying stocks 

are “worth more alive than dead.” 

 If it never pays to exercise a call option 

before expiration, the right to exercise 

early actually must be valueless. We con-

clude that the values of otherwise identi-

cal American and European call options 

on stocks paying no dividends are equal. 

This simplifies matters, because any valu-

ation formula that applies to the European 

call, for which only one exercise date 

need be considered, also must apply to an 

American call. 

 

As most stocks do pay dividends, you 

may wonder whether this result is just a theo-

retical curiosity. It is not: Reconsider our 

argument and you will see that all that we really require is that the stock pay no dividends 

 until the option expires.  This condition will be true for many real-world options.  

Call Value

 Lower 

Bound

5 Adjusted Intrinsic

    Value

5 S

0

 

2 PV(X) 2 PV(D)

Upper Bound 

5

 S

0

Allowable Range

PV(X) 

1 PV(D)

S

0

 Figure 21.2 

Range of possible call option values  

Value of Call for

Given Stock Price

C

S

0

PV(X) 

1 PV(D)

 Figure 21.3 

Call option value as a function of the 

 current stock price  

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7/27/13   1:45 AM

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