Answer: SGD 8.45

## 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

Author: LeetQuiz .