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Answer: USD 0.32
## 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.
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An analyst has been asked to estimate the VaR of a long position in a put option on the stock of Big Pharma, Inc. The stock is trading at USD 26.00 with a daily volatility of 1.5%, and the option is at-the-money with a delta of −0.5. Using the delta-normal method, which of the following choices is closest to the 1-day 95% VaR of the option position?
A
USD 0.32
B
USD 0.45
C
USD 0.64
D
USD 0.91