
Explanation:
The minimum value for a European-style call option, , is given by:
\max[0,\ S_T - X / (1 + R_F)^T] = \max[0,\ 86 - 80 / (1.03)^{3/12}] = \`$6.59`An American-style call option must be worth at least as much as an otherwise identical European-style call option and has the same minimum value. Note that this fact alone limits the possible correct responses to Choices A and D. Since the American-style call is in-the-money and therefore must be worth more than the $6 difference between the strike price and the stock price, you can eliminate Choice A and select Choice D without calculating the exact minimum value.
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Question 16
What are the minimum values of an American-style and a European-style 3-month call option with a strike price of $80 on a non-dividend-paying stock trading at $86 if the risk-free rate is 3%?
A
American: $6.00 | European: $6.00
B
American: $5.96 | European: $6.00
C
American: $6.00 | European: $6.59
D
American: $6.59 | European: $6.59
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