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比夏 · 2024年09月07日

没懂解析里AE的计算公式

  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2020033002000004

问题如下：

A bank granted Client A a total credit facility of $500,000, of which 70% is currently outstanding. The client's probability of default for the following year is estimated to be 2%, the loss given default is 50%, and the standard deviation of loss given default is 30%. The undrawn portion at the time of default assumes a 50% withdrawal. What is the bank's best estimate of expected and unexpected losses (standard deviation) ?

选项：

A.

EL = $3500, UL = $55,229

B.

EL = $3500, UL = $28,649

C.

EL = $4250, UL = $67,064

D.

EL = $4250, UL = $34,788

解释：

D is correct.

考点：Risk Contribution

解析：

AE=70%x$500,000+50%*30%*$500,000=$425,000

EL=425,000*2%*50%=4250

UL的公式如下：

UL=AE∗p×σLGD2+p×(1−p)×LGD2UL=AE\ast\sqrt{p\times\sigma_{LGD}^2+p\times{(1-p)}\times{LGD}^2}

代入公式，有

UL=34,788

AE=70%x$500,000+50%*30%*$500,000=$425,000


解析里这条公式为什么要两部分相加？

我理解不是只计算后面那部分就可以了吗？

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2 个答案

pzqa27 · 2024年09月10日

嗨，努力学习的PZer你好：


没借出去的敞口也需要计算吗？

这里题目说了“ The undrawn portion at the time of default assumes a 50% withdrawal”，也就是说还没借出去的30%那部分，要记入AE的是50%的withdrawal。（withdrawal是被借款人取走的，就是bank可能损失掉的部分）。既然有50%会被withdrawal，那么就是有风险的，因此是要被计入到AE中。


这部分的知识点在哪个视频里有提到吗？还是这个题目的特殊性？

这里可以认为是这个题目的特殊性。

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pzqa27 · 2024年09月09日

嗨，爱思考的PZer你好：


AE是这样的计算的，首先是银行已经借出去的（outstanding）的部分70% * 500000。


然后没借出去的部分有30%, 这些没借出去的部分的敞口是按照LGD的50%来计算，也就是30% * 50% * 500000。


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努力的时光都是限量版，加油！

比夏 · 2024年09月09日

没借出去的敞口也需要计算吗？ 这部分的知识点在哪个视频里有提到吗？还是这个题目的特殊性？

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