Answer: Lower bound USD 5.00, upper bound USD 5.13

## Explanation The correct answer is **B** because the lower and upper bounds for American options can be derived from the put-call parity inequality: $$ S_0 - K \leq (C - P) \leq S_0 - Ke^{-rT} $$ Where: - $S_0 = 40$ (current stock price) - $K = 35$ (strike price) - $r = 1.5\% = 0.015$ (risk-free rate) - $T = 3/12 = 0.25$ years (time to maturity) **Calculations:** - **Lower bound**: $S_0 - K = 40 - 35 = 5$ - **Upper bound**: $S_0 - Ke^{-rT} = 40 - 35e^{-0.015 \cdot 0.25} = 40 - 35e^{-0.00375} = 40 - 35 \cdot 0.99626 = 40 - 34.87 = 5.13$ Therefore, the bounds are: $$ 5 \leq (C - P) \leq 5.13 $$ **Alternative approach using American option bounds:** | Option | Minimum Value | Maximum Value | |--------|---------------|---------------| | American Call | $C \geq \max(0, S_0 - Ke^{-rT}) = 5.13$ | $S_0 = 40$ | | American Put | $P \geq \max(0, K - S_0) = 0$ | $K = 35$ | Subtracting the put values from the call values: - Minimum difference: $5.13 - 35 = -29.87$ (but this is not meaningful) - Maximum difference: $40 - 0 = 40$ (but this is not meaningful) The correct approach is to use the put-call parity bounds for American options, which gives us the range $5 \leq (C - P) \leq 5.13$.

Author: LeetQuiz .