Explanation

This question requires using the put-call parity formula for options with dividends:

Put-Call Parity with Dividends: $C - P = S_0 - D \cdot e^{-r \cdot t_d} - K \cdot e^{-r \cdot T}$

Where:

• $C = 3$ (call price)
• $P$ = put price (what we're solving for)
• $S_0 = 24$ (current stock price)
• $D = 1$ (dividend)
• $r = 0.05$ (continuously compounded risk-free rate)
• $t_d = 0.25$ (3 months = 0.25 years until dividend)
• $T = 0.5$ (6 months = 0.5 years until option expiration)
• $K = 25$ (strike price)

Step 1: Calculate present value of dividend $D \cdot e^{-r \cdot t_d} = 1 \cdot e^{-0.05 \cdot 0.25} = e^{-0.0125} = 0.9876$

Step 2: Calculate present value of strike price $K \cdot e^{-r \cdot T} = 25 \cdot e^{-0.05 \cdot 0.5} = 25 \cdot e^{-0.025} = 25 \cdot 0.9753 = 24.3825$

Step 3: Apply put-call parity $C - P = S_0 - D \cdot e^{-r \cdot t_d} - K \cdot e^{-r \cdot T}$ $3 - P = 24 - 0.9876 - 24.3825$ $3 - P = -1.3701$ $-P = -1.3701 - 3$ $-P = -4.3701$ $P = 4.3701$

The put option value is approximately USD 4.37, which matches option C.

Verification:

• Without the dividend adjustment, the put price would be different
• The dividend reduces the effective stock price in the put-call parity relationship
• The calculation properly accounts for the timing of the dividend payment