Investments, tenth edition

  

  udS     5   $104.50  

  uuS  

 0 

     5   $121  

 Buy 2 shares at price  uS  

0

   5  $110 

 $209  

 $242 

 Write 3 calls at price  C  

 u 

  

      0  

       2  33  

    TOTAL  

 $209  

$209 

The portfolio must have a current market value equal to the present value of $209:

2 3 110 2 3C

u

 5 $209/1.05 5 $199.047

Solve to find that  C  

 u 

   5  $6.984. 

 Next we find the value of  C  

 d 

 . It is easy to see that this value must be zero. If we reach 

this point (corresponding to a stock price of $95), the stock price at option expiration 

will be either $104.50 or $90.25; in either case, the option will expire out of the money. 

(More formally, we could note that with  C  

 ud 

   5   C  

 dd 

   5  0, the hedge ratio is zero, and a 

portfolio of zero shares will replicate the payoff of the call!) 

 Finally, we solve for C using the values of  C  

 u 

  and  C  

 d 

 . Concept Check 4 leads you 

through the calculations that show the option value to be $4.434. 

 Example  21.1 

Binomial Option Pricing 

bod61671_ch21_722-769.indd   732

bod61671_ch21_722-769.indd   732

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7/27/13   1:45 AM

Final PDF to printer

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  C H A P T E R  

2 1

 Option 

Valuation 

733