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20 July, 11:35

The price of Chive Corp. stock will be either $86 or $119 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 $97. What is the value of the call option if the exercise price is $85 per share? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.) b. Suppose the exercise price is $115 and the current price of the company's stock is $97. What is the value of the call option now? (Do not round intermediate calculations and round your answer to 2 decimal places, e. g., 32.16.)

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  1. 20 July, 11:40
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    Answer and Explanation:

    a). Step 1: Calculate the option value at expiration based upon your assumption of a 50% chance of increasing to $119 and a 50% chance of decreasing to $86.

    The two possible stock prices are:

    S + = $119 and S - = $86. Therefore, since the exercise price is $85, the corresponding two possible call values are:

    Cu = $34 and Cd = $1.

    Step 2: Calculate the hedge ratio:

    (Cu - Cd) / (uS0 - dS0) = (34 - 1) / (119 - 86) = 33/33 = 1

    Step 3: Form a riskless portfolio made up of one share of stock and one written calls. The cost of the riskless portfolio is:

    (S0 - C0) = 97 - C0

    and the certain end-of-year value is $86.

    Step 4: Calculate the present value of $86 with a one-year interest rate of 5%:

    $86/1.05 = $81.90

    Step 5: Set the value of the hedged position equal to the present value of the certain payoff:

    $97 - C0 = $81.90

    C0 = $97 - $81.90 = $15.10

    b). Step 1: Calculate the option value at expiration based upon your assumption of a 50% chance of increasing to $119 and a 50% chance of decreasing to $86.

    The two possible stock prices are:

    S + = $119 and S - = $86. Therefore, since the exercise price is $115, the corresponding two possible call values are:

    Cu = $4 and Cd = $0.

    Step 2: Calculate the hedge ratio:

    (Cu - Cd) / (uS0 - dS0) = (4 - 0) / (119 - 86) = 4/33

    Step 3: Form a riskless portfolio made up of four shares of stock and thirty three written calls. The cost of the riskless portfolio is:

    (4S0 - 33C0) = 4 (97) - 33C0 = 388 - 33C0

    and the certain end-of-year value is $86.

    Step 4: Calculate the present value of $86 with a one-year interest rate of 5%:

    $86/1.05 = $81.90

    Step 5: Set the value of the hedged position equal to the present value of the certain payoff:

    $388 - 33C0 = $81.90

    33C0 = $388 - $81.90

    C0 = $306.10 / 33 = $9.28
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