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云梦 · 2021年08月08日

这题的公式基本原理还是不太明白

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000048

问题如下：

A portfolio manager owns a portfolio of options on a non-dividend paying stock RTX. The portfolio is made up of 10,000 deep in-the-money call options on RTX and 50,000 deep out-of-the money call options on RTX. The portfolio also contains 20,000 forward contracts on RTX. RTX is trading at USD 100. If the volatility of RTX is 30% per-year, which of the following amounts would be closest to the 1-day VaR of the portfolio at the 95 percent confidence level, assuming 252 trading days in a year?

选项：

A.

USD 932

B.

USD 93,263

C.

USD 111,122

D.

USD 131,892

解释：

B is correct.

考点 ： Mapping to Option Position

解析 ： We need to map the portfolio to a position in the underlying stock RTX. A deep in-the-money call has a delta of approximately 1, a deep out-of-the-money call has delta of approximately 0 and forwards have a delta of 1. The net portfolio has a delta of about 30,000 and is approximately gamma neutral. The 1-day VaR estimate at 95 percent confidence level is computed as follows:

α×S×∆×σ×SQRT(1/T)=1.645×100×30000×0.3×SQRT(1/252)=93263

老师好，看了之前的对这题的回复还是不太明白。这题是用VAR(dc)=|Δ|*VAR(ds)这个公式算的吧？那|Δ|=？,VAR(ds)=? 能不能再分步骤具体讲解一下。VAR(ds)是不是应该用-μ+Zα*σ来计算？其中Zα=1.645 ,σ=题中的σ/根号天数。

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品职答疑小助手雍 · 2021年08月08日

嗨，爱思考的PZer你好：


不要看那个回答了，也不用套公式去对应。

非要套进公式里的话，只是说公式里mapping的结果是var（dc），一个表示符号而已。

把option和forward的delta mapping完，加起来就是portfolio的var了。

计算过程如下：

deep ITM的call的delta是1，OTM的call的delta是0，forward的delta是1.组合整体的delta就是30000。

日波动率计算跟你说的一样0.3/根号下252。

那var就是1.645*100*30000*日波动率就行了。

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