Answer: USD 3.63

## Explanation This question involves applying the **put-call parity** formula adjusted for dividends. The standard put-call parity formula is: \[ c + \text{PV}(K) = p + S_0 \] However, when there are dividends, we need to adjust for the present value of dividends: \[ c = S_0 + p - \text{PV}(K) - \text{PV}(D) \] **Given:** - Put price (p) = USD 3.00 - Stock price (S₀) = USD 26.00 - Strike price (K) = USD 25.00 - Dividend (D) = USD 1.00 - Time to dividend (t) = 3 months = 0.25 years - Time to expiration (T) = 6 months = 0.5 years - Risk-free rate (r) = 5% = 0.05 **Calculations:** 1. **Present Value of Strike Price:** \[ \text{PV}(K) = K \cdot e^{-rT} = 25.00 \cdot e^{-0.05 \cdot 0.5} = 25.00 \cdot e^{-0.025} = 25.00 \cdot 0.9753 = 24.3827 \] 2. **Present Value of Dividend:** \[ \text{PV}(D) = D \cdot e^{-rt} = 1.00 \cdot e^{-0.05 \cdot 0.25} = 1.00 \cdot e^{-0.0125} = 1.00 \cdot 0.9876 = 0.9876 \] 3. **Call Price Calculation:** \[ c = S_0 + p - \text{PV}(K) - \text{PV}(D) = 26.00 + 3.00 - 24.3827 - 0.9876 = 3.6297 \] The calculated call price is approximately USD 3.63, which matches option C. **Key Points:** - Put-call parity must be adjusted for dividends - The dividend is discounted from its payment date (3 months) - The strike price is discounted from the option expiration date (6 months) - This ensures no arbitrage opportunities exist in the market

Author: LeetQuiz .