Answer: USD 4.37

## 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

Author: LeetQuiz .