The correct answer to the question is B: 5.00 and 5.13. This is based on the put-call parity principle, which is a fundamental concept in options pricing. The put-call parity states that the price of a call option and a put option with the same strike price and expiration date should be related in a specific way.

For American options, which can be exercised at any time before expiration, the put-call parity can be expressed as an inequality:

$-K \leq (C - P) \leq S_0 - Ke^{-rT}$

Where:

• $C$ is the price of the call option,
• $P$ is the price of the put option,
• $K$ is the strike price,
• $S_0$ is the current stock price,
• $r$ is the risk-free rate, and
• $T$ is the time to maturity.

In this scenario, the stock price $S_0$ is USD 40, the strike price $K$ is USD 35, the risk-free rate $r$ is 1.5%, and the time to maturity $T$ is 3 months (or 0.25 years). Plugging these values into the inequality gives us:

$-35 \leq (C - P) \leq 40 - 35e^{-0.015 \times \frac{3}{12}}$

Simplifying the upper bound:

$5 \leq (C - P) \leq 5.13$

This means that the difference between the call and put option prices must be at least 5 and at most 5.13.

Additionally, the minimum and maximum values for American options can be determined as follows:

• The American call option $C$ has a minimum value of $max(0, S_0 - Ke^{-rT})$, which in this case is $max(0, 40 - 35e^{-0.015 \times \frac{3}{12}}) = 5.13$.
• The American put option $P$ has a minimum value of $max(0, K - S_0)$, which is $max(0, 35 - 40) = 0$.

Subtracting the put option value from the call option value confirms the bounds:

$5 \leq C - P \leq 5.13$

This analysis aligns with the explanation provided in the file content, confirming that option B is the correct answer.