Answer: 5.00

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.

Author: LeetQuiz Editorial Team