NO.PZ2023091701000083
问题如下：
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?
选项：
A.USD 0.32 B.USD 0.45 C.USD 0.64 D.USD 0.91解释：
A is correct. The variance of a portfolio with respect to its n risk factors is
where ai is the delta of the portfolio with respect to the ith risk factor and σi is the standard deviation of theith risk factor. The option’s standard deviation is therefore
the average change in a linear portfolio is zero. Therefore, when U equals 1.645, the point
of the standard normal distribution corresponding to the 95th percentile, the deltanormal
VaR of the option at the 95% confidence level is
𝜎p*𝑈 = 0.195*1.645 = 𝑈𝑆𝐷 0.3208
B is incorrect. USD 0.45 is the 1-day 99% VaR of the option.
C is incorrect. USD 0.64 is the 1-day 95% VaR if the delta of the option is 1.0.
D is incorrect. USD 0.91 is the 1-day 99% VaR of the option if the delta of the option is 1.0
