Explanation:

With everything else held constant:

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.

Q-179.4. EACH of the following is true about the RISK-FREE RATE, ceteris paribus, with respect to option value EXCEPT:

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MManit

Last updated: April 18, 2026 at 11:32

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

28.6%

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

42.9%

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

14.3%

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

14.3%

Financial Risk Manager Part 1