Answer: 5.00

The question is related to the valuation of American-style call and put options using the put-call parity principle. The put-call parity is a fundamental relationship in options pricing that states that the price of a call option should be equivalent to the price of a put option plus the present value of the difference between the exercise price and the current stock price. Given the scenario: - American-style call and put options with 3 months to maturity. - Non-dividend-paying stock at USD 40. - Strike price for both options at USD 35. - Risk-free rate at 1.5%. The put-call parity for American options can be expressed as an inequality: \[ So - Ke^{-rT} \leq C - P \leq So - K \] Where: - \( C \) is the price of the call option. - \( P \) is the price of the put option. - \( So \) is the current stock price. - \( K \) is the strike price. - \( r \) is the risk-free rate. - \( T \) is the time to maturity. Plugging in the given values: - \( So = 40 \) - \( K = 35 \) - \( r = 0.015 \) (1.5% as a decimal) - \( T = \frac{3}{12} \) (3 months as a fraction of a year) The lower bound of the difference \( (C - P) \) is straightforward: \[ 40 - 35 = 5 \] For the upper bound, we calculate the present value factor: \[ e^{-0.015 \times \frac{3}{12}} \approx 0.995 \] So the upper bound is: \[ 40 - 35 \times 0.995 \approx 5.13 \] Thus, the bounds on the difference between the prices of the call and put options are: \[ 5 \leq C - P \leq 5.13 \] The correct answer is B, which states that the lower bound is 5.00 USD and the upper bound is 5.13 USD. This is consistent with the put-call parity for American options and the given parameters.

Author: LeetQuiz Editorial Team