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Answer: USD 0.28
## Explanation Using the delta-normal method for VaR calculation: - **Stock price (S)**: USD 23 - **Daily volatility (σ)**: 1.5% = 0.015 - **Delta (Δ)**: -0.5 - **Z-score for 95% confidence**: 1.645 **VaR formula for options**: \[ \text{VaR} = |\Delta| \times S \times \sigma \times Z \] \[ \text{VaR} = 0.5 \times 23 \times 0.015 \times 1.645 \] \[ \text{VaR} = 0.5 \times 23 \times 0.024675 \] \[ \text{VaR} = 0.5 \times 0.567525 \] \[ \text{VaR} = 0.2837625 \] Rounded to USD 0.28 **Key points**: - The absolute value of delta is used since VaR represents potential loss - For a long put position, the risk comes from the stock price increasing (delta negative) - The delta-normal method linearizes the option's price sensitivity
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You have been asked to estimate the VaR of an investment in Big Pharma Inc. The company's stock is trading at USD 23 and the stock has a daily volatility of 1.5%. Using the delta-normal method, the VaR at the 95% confidence level of a long position in an at-the-money put on this stock with a delta of -0.5 over a 1-day holding period is closest to which of the following choices?
A
USD 0.28
B
USD 0.40
C
USD 0.57
D
USD 2.84