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Answer: USD 0.32
A is correct. The variance of a portfolio with respect to its n risk factors is \( a^2 \sum_{i=1}^{n} P_i Q_i \), where \( a_i \) is the delta of the portfolio with respect to the ith risk factor and \( \sigma_i \) is the standard deviation of the ith risk factor. The option's standard deviation is therefore \( \sqrt{(-0.5)^2 * (0.015 * 26)^2} = 0.195 \). A common assumption is that the mean change in each risk factor is zero and therefore the average change in a linear portfolio is zero. Therefore, when \( Z \) equals 1.645, the point of the standard normal distribution corresponding to the 95th percentile, the delta-normal VaR of the option at the 95% confidence level is \( 0.195 * 1.645 = USD 0.3208 \).
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A financial analyst must calculate the 1-day 95% Value at Risk (VaR) for holding a put option on the stock of Big Pharma, Inc. The stock is currently valued at USD 26.00 and exhibits a daily volatility rate of 1.5%. The put option is an at-the-money option with a delta of -0.5. Using the delta-normal approach, identify the option that is closest to the calculated 1-day 95% VaR for this position.
A
USD 0.32
B
USD 0.45
C
USD 0.64
D
USD 0.91