The price of Swearengen, Inc., stock will be either $66 or $88 at the end of the
ID: 2796216 • Letter: T
Question
The price of Swearengen, Inc., stock will be either $66 or $88 at the end of the year. Call options are available with one year to expiration. T-bills currently yield 5 percent.
a. Suppose the current price of the company's stock is $77. What is the value of the call option if the exercise price is $62 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Call value $
b. Suppose the current price of the company's stock is $77. What is the value of the call option if the exercise price is $72 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Call value $
Explanation / Answer
a. The stock payoff is either 66 or 88. The option payoff is either (66-62)= 4 or 88-62 = 26
The hedge ratio = 26-4/88-66 = 1
The risk free payoff = 66*1 = $66
Hence option worth = 77*1 - 66/1.05
= $14.14
PART b
The stock payoff is either 66 or 88. The option payoff is either 0 or 88-72 = 16
The hedge ratio = 16-0/88-66 = 0.7273
The risk free payoff = 66*0.7273 = $48
Hence option worth = 77*0.7273 - 48/1.05
= $10.29
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