Explanation

The correct price of the European put option using the Black-Scholes-Merton model for a dividend-paying stock is calculated using the formula:

$p = Ke^{-rT} \mathcal{N}(-d_2) - S_0 e^{-qT} \mathcal{N}(-d_1)$

Where:

• $S_0 = 82$ (current stock price)
• $K = 85$ (strike price)
• $T = 0.5$ years (6 months)
• $r = 0.025$ (risk-free rate)
• $q = 0.02$ (dividend yield)
• $\mathcal{N}(-d_1) = 0.5205$
• $\mathcal{N}(-d_2) = 0.6040$

Calculation: $p = 85 \times e^{-0.025 \times 0.5} \times 0.6040 - 82 \times e^{-0.02 \times 0.5} \times 0.5205$ $p = 85 \times e^{-0.0125} \times 0.6040 - 82 \times e^{-0.01} \times 0.5205$ $p = 85 \times 0.98758 \times 0.6040 - 82 \times 0.99005 \times 0.5205$ $p = 50.69 - 42.24 = 8.45$

Why other options are incorrect:

• A (SGD 5.11): This results from switching K and S in the formula
• B (SGD 5.73): This uses an incorrect formula $p = S_0 \mathcal{N}(-d_2) - K e^{-qT} \mathcal{N}(-d_1)$
• D (SGD 8.86): This incorrectly treats the dividend as discrete rather than continuous