Answer: Scenario B

## Explanation For American options on non-dividend-paying stocks, the put-call parity relationship leads to the 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) **Calculating the bounds:** **Lower Bound:** $$ S_0 - K = 40 - 35 = 5 $$ **Upper Bound:** $$ S_0 - Ke^{-rT} = 40 - 35e^{-0.015 \times 0.25} $$ $$ = 40 - 35e^{-0.00375} $$ $$ = 40 - 35 \times 0.99626 $$ $$ = 40 - 34.87 = 5.13 $$ Therefore, the bounds are: $$ 5 \leq (C - P) \leq 5.13 $$ This corresponds to **Scenario B** in the table. **Alternative approach using individual option bounds:** For American options: - **Call minimum:** $C \geq \max(0, S_0 - Ke^{-rT}) = \max(0, 40 - 34.87) = 5.13$ - **Call maximum:** $C \leq S_0 = 40$ - **Put minimum:** $P \geq \max(0, K - S_0) = \max(0, 35 - 40) = 0$ - **Put maximum:** $P \leq K = 35$ Subtracting put values from call values gives the same result: $$ 5.13 - 35 \leq C - P \leq 40 - 0 $$ $$ -29.87 \leq C - P \leq 40 $$ However, the tighter bounds from put-call parity are more precise: $5 \leq C - P \leq 5.13$

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