Your group has been assigned task of determining what value to place on call opt
ID: 2776457 • Letter: Y
Question
Your group has been assigned task of determining what value to place on call option for your firm. The current stock price per share is $54.52. Six months from now management believes the stock price will either fall by 25% or rise by 33%. Using this information, determine what a 6 month call should be valued at if the risk free rate of return is at 2% annually. Banks will loan you at .5% over the risk-free rate. Using option equivalents from common stock and borrowing, determine the price of the call option to submit to management.
Explanation / Answer
if 33% increase => 72.51
if fall by 25% => 40.89
Replecating portfolio method = Call option payoff = 72.51-54.52 =>17.99 or 0
72.51(A) + 1.02(B) =17.99, 40.89(A) + 1.02(B) =0
=> A = 0.569 and B = -22.81
call option price (current) => 0.569*(54.52) - 22.81
=> $8.21
Risk- neutral valuation: = 54.52 = [x(72.51) + (1-x)40.89]/1.02) hence x = 0.47 and (1-x) = 0.53
Call option value = [(0.47)(17.99) + (0.53)(0)]/(1.02) = $8.21
call option value = $8.21
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