Investments, tenth edition

  Dividends and Call Option Valuation 

 We noted earlier that the Black-Scholes call option formula applies to stocks that do not 

pay dividends. When dividends are to be paid before the option expires, we need to adjust 

the formula. The payment of dividends raises the possibility of early exercise, and for most 

realistic dividend payout schemes the valuation formula becomes significantly more com-

plex than the Black-Scholes equation. 

 We can apply some simple rules of thumb to approximate the option value, however. 

One popular approach, originally suggested by Black, calls for adjusting the stock price 

downward by the present value of any dividends that are to be paid before option expi-

ration.  

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   Therefore, we would simply replace  S  

0

  with  S  

0

      2  PV(dividends) in the Black-

Scholes formula. Such an adjustment will take dividends into account by reflecting their 

eventual impact on the stock price. The option value then may be computed as before, 

assuming that the option will be held to expiration.   

 In one special case, the dividend adjustment takes a simple form. Suppose the underlying 

asset pays a continuous flow of income. This might be a reasonable assumption for options 

on a stock index, where different stocks in the index pay dividends on different days, so that 

dividend income arrives in a more or less continuous flow. If the dividend yield, denoted  d ,  is 

constant, one can show that the present value of that dividend flow accruing until the option 

expiration date is  S  

0

  (1  2   e  

 2  d  T 

 ). (For intuition, notice that  e  

 2  d  T 

  approximately equals 1  2   d  T,  

so the value of the dividend is approximately  d  TS  

0

 .) In this case,  S  

0

   2  PV(Div)  5   S  

0

   e  

 2  d  T 

 ,  and 

we can derive a Black-Scholes call option formula on the dividend-paying asset simply by 

substituting  S  

0

   e  

 2  d  T 

  for  S  

0

  in the original formula. This approach is used in Spreadsheet 21.1. 

 These procedures yield a very good approximation of option value for European call 

options that must be held until expiration, but they do not allow for the fact that the holder 

of an American call option might choose to exercise the option just before a dividend. The 

current value of a call option, assuming that it will be exercised just before the ex-dividend 

date, might be greater than the value of the option assuming it will be held until expiration. 

Although holding the option until expiration allows greater effective time to expiration, 

  

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 Fischer Black, “Fact and Fantasy in the Use of Options,”  Financial Analysts Journal  31 (July–August 1975).