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小猫批脸 · 2023年01月07日

这道题是不是只学了nonparametric和parametric 是不是解答不了？

  1. FRM II
  2. Market Risk Measurement And Management

NO.PZ2018122701000018

问题如下：

The bank’s trading book consists of the following two assets:

Correlation (A, B) = 0.2

How would the daily VaR at 99% level change if the bank sells $50 worth of asset A and buys $50 worth of asset B?

Assume there are 250 trading days in a year.

选项：

A.

$0.2286

B.

$0.4776

C.

$0.7705

D.

$0.7798

解释：

B is correct.

考点 ： Parametric Estimation Approaches

解析 ： The trade will decrease the VaR by 0.4776。

易错点：求daily VaR，但题干给的是annual return。

t=0，组合由$100A+$50B构成，μP =13.33%, 由年转化为天，13.33%/250=0.0533%.

σP =19.15%, 由年转化为天, 19.15%/SQRT(250)=1.2111%

daily 99%VaR=（2.33*1.2111%-0.0533%）*$150=$4.1528

t=1，组合由$50A+$100B构成，μP =16.66%, 由年转化为天，16.66%/250=0.0667%.

σP =17.08%, 由年转化为天, 17.08%/SQRT(250)=1.0801%

daily 99%VaR=（2.33*1.0801%-0.0667%）*$150=$3.6749

所以$4.1528-$3.6749=0.4779，最接近的是B选项。

不太懂老师，我只学了参数法和非参数法，不太懂整体思路。是不是要和衍生品结合起来？

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1 个答案

DD仔_品职助教 · 2023年01月08日

嗨，从没放弃的小努力你好：


同学你好，

学习了参数法之后就能做出来这个题，只不过这里求的是组合的VAR，参数法求VAR需要用到均值μ以及σ的数据，所以这里的难点是求组合的均值以及组合σ。

我们首先明确要求的是VAR的变化量，所以要分别求出0时刻和1时刻的VAR，然后进行相减。

其次就分别计算这两个时刻的VAR，也就是求组合均值与σ。

这里使用的是dollar形式的均值与σ，

组合均值=valueA*returnA+valueB*returnB

组合σ=valueA^2*sigmaA^2+valueB^2*sigmaB^2+2*valueA*valueB*sigmaA*sigmaB*相关系数

组合的VAR=组合均值-Z*组合sigma的绝对值

详细步骤如下图：

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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