Explanation

Using the delta-normal method for VaR calculation:

Step 1: Calculate the option's standard deviation

• Stock price: USD 26.00
• Daily volatility: 1.5% = 0.015
• Option delta: -0.5

$$\sigma_p = |\delta| \times \sigma_i \times S = |-0.5| \times 0.015 \times 26 = 0.195$$

Step 2: Calculate 1-day 95% VaR

• Z-score for 95% confidence level: 1.645

$$\text{VaR} = \sigma_p \times Z = 0.195 \times 1.645 = \text{USD } 0.3208 \approx \text{USD } 0.32$$

Why other options are incorrect:

• B (USD 0.45): This is the 1-day 99% VaR (using Z = 2.326: 0.195 × 2.326 = 0.453)
• C (USD 0.64): This would be the 1-day 95% VaR if delta = 1.0 (0.015 × 26 × 1.645 = 0.641)
• D (USD 0.91): This would be the 1-day 99% VaR if delta = 1.0 (0.015 × 26 × 2.326 = 0.907)

The delta-normal method linearizes the option's price sensitivity using delta, making it suitable for short time horizons where gamma effects are minimal.