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Cooljas · 2024年04月19日

为什么1.5%不用开根号啊?

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



1 个答案

李坏_品职助教 · 2024年04月19日

嗨,努力学习的PZer你好:


题目给的条件是daily volatility ,在FRM的官方出题规范中,volatility指的是标准差,不是方差。所以不用开根号。

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