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Answer: A European put option on a stock paying a 1.60% dividend with a 3.0% risk-free rate has a lower bound of zero.
The true statement is **C**. The European put option on a 1.60% dividend stock with a 3.0% risk-free rate has a lower bound of zero. - For a European **call** on a non-dividend-paying stock, the lower bound is positive: $50.00 - 50.00 e^{-0.03\times 0.5} = $0.74. - For a European **call** on a dividend-paying stock, the lower bound is reduced by the dividend amount: $50.00 - $0.40 - 50.00 e^{-0.03\times 0.5} = $0.34. - For a European **put** on a dividend-paying stock with a 3.0% risk-free rate, the lower bound is max\[0, $0.40 + 50.00 e^{-0.03\times 0.5} - $50.00\] = max\[0, -0.34\] = **0**. - For the same put with a 0% risk-free rate, the lower bound is max\[0, $0.40 + 50.00 e^{0\times 0.5} - $50.00\] = **$0.40**.
Author: Manit Arora
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Q-725.2 Which of the following statements about the lower bounds of European option values is true?
A
A European call option on a non-dividend-paying stock with a 3.0% risk-free rate has a lower bound of zero.
B
A European call option on a stock paying a 1.60% dividend with a 3.0% risk-free rate has a lower bound of zero.
C
A European put option on a stock paying a 1.60% dividend with a 3.0% risk-free rate has a lower bound of zero.
D
A European put option on a stock paying a 1.60% dividend with a 0% risk-free rate has a lower bound of zero.
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