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: $5 \leq C - P \leq 5.13$