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Answer: a) An increase in the risk-free rate must increase the lower bound (minimum value) of a European PUT option on a non-dividend-paying stock
With everything else held constant: - A higher **risk-free rate** reduces the present value of the strike price. - That makes **calls** more valuable. - That makes **puts** less valuable. For lower bounds: - European call lower bound on a non-dividend-paying stock: \(S_0 - Ke^{-rT}\). A higher \(r\) increases this bound. - European put lower bound on a non-dividend-paying stock: \(Ke^{-rT} - S_0\) (when positive). A higher \(r\) decreases this bound. Thus, statement **A** is false, because increasing the risk-free rate does **not** increase the lower bound of a European put; it decreases it. So the exception is **A**.
Author: Manit Arora
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Q-179.4. EACH of the following is true about the RISK-FREE RATE, ceteris paribus, with respect to option value EXCEPT:
A
a) An increase in the risk-free rate must increase the lower bound (minimum value) of a European PUT option on a non-dividend-paying stock
B
b) An increase in the risk-free rate must increase the lower bound (minimum value) of a European CALL option on a non-dividend-paying stock
C
c) An increase in the risk-free rate will increase the value of an American and European CALL on either dividend- or non-dividend-paying stock
D
d) An increase in the risk-free rate will decrease the value of an American and European PUT on either dividend- or non-dividend-paying stock
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