Answer-first summary for fast verification
Answer: If the option is European (either a call or a put), the lower bound (aka, minimum value) simplifies to the option's intrinsic value
The false statement is **D**. - **A is true:** A lower risk-free rate increases the present value of the strike, which makes puts more valuable. - **B is true:** A lower risk-free rate generally reduces call value because the PV of the strike is higher. - **C is true:** When interest rates fall to zero, the benefit from early exercise is reduced for both calls and puts, so early exercise becomes less attractive. - **D is false:** For European options on a dividend-paying stock, the lower bound does **not** simply become intrinsic value when the risk-free rate is zero. - For a European call, the lower bound is: \[ \max(0, S - PV(D) - K) \] - For a European put, the lower bound is: \[ \max(0, K + PV(D) - S) \] These include dividends and do not reduce to intrinsic value unless dividends are zero.
Author: Manit Arora
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Question-726.2. Assume an option has a strike price of $50.00 and its time to expiration is six months (0.5 years) while the stock pays a dividend. Each of the following implications is true, ceteris paribus, if the risk-free rate reduces from 3.0% to zero EXCEPT which is FALSE if the risk-free rate reduces to zero?
A
If the option is put (either American or European), its price will increase
B
If the option is a call (either American or European), its price will decrease
C
If the option is American (either a call or a put), the early exercise feature becomes relatively LESS attractive
D
If the option is European (either a call or a put), the lower bound (aka, minimum value) simplifies to the option's intrinsic value
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