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翟延昕 · 2022年03月03日

根据谨慎性原则，为什么WCL不是44？而是24

  1. FRM II
  2. Credit Risk Measurement And Management

NO.PZ2020033002000008

问题如下：

There is a bond portfolio consisted with two bonds. bond A and bond B .The values of bond A and bond B are $60 millions and $40 millions respectively. The one-year probabilities of default and the recovery rate of bond A are 5% and 60% respectively, while for bond B are 7% and 50%. Calculate the one-year expected credit loss of this portfolio. Give an assumption that the probability of joint default is 0.7% and the default correlation is 20%.

what is the best estimate of the credit VaR at a 98% confidence level?

选项：

A.

USD 17,400,000

B.

USD 21,400,000

C.

USD 41,400,000

D.

USD 44,000,000

解释：

B is correct.

考点：Credit VaR

解析：

Bond A 违约的损失是60*（1-60%）=24 million

Bond B违约的损失是40*（1-50%）=20million

A、 B同时违约的概率是 0.7% 24+40=44 million

Bond A 违约但是bond B不违约的概率是 5%-0.5%=4.5%

Bond B违约但是bond A不违约的概率是7%-0.5%=6.5%

根据谨慎性原则 98% confidence WCL=24million

credit VaR=24-2.6=21.4 million

WCL应该是44吧



添加评论
李晨 · 2022年03月19日

老师好，我也不太明白，为什么WCL不是取44而是24. 上图很清楚98%是在44和24之间的，谨慎原则应该是44才对？感谢。

4 个答案

品职答疑小助手雍 · 2022年03月19日

同学你好，请认真回答里的截图和解析，应该能明本题如何定义Var了。我的图里很清楚了画出了98%是处于24cover的区域下的，所以98%的var就是24。

品职答疑小助手雍 · 2022年03月09日

同学你好，截图已经明确表达了24涵盖的就是94.8%到99.3%的区间，44涵盖的是99.3%到100%的区间，不太明白哪个点会表达出24盖不住的意思。

如果你看完图还是觉得盖不住，那麻烦你先指出24涵盖的应该是哪个区间，我看看是哪里出问题了。

品职答疑小助手雍 · 2022年03月05日

同学你好，横轴对应的是概率，图里我绿色标注的损失意思就是这些损失数值涵盖的区间，比如44就是涵盖99.3%到100%的这一段，24涵盖的是94.8%到99.3%的区间，98%落在这个区间里，所以98%的var就是24。

翟延昕 · 2022年03月08日

P(loss≤24）=94.8% 94.8%-99.3%的区间 24盖不住吧

品职答疑小助手雍 · 2022年03月04日

同学你好，图画错了，横轴标的应该是概率，尾部44的损失概率分位点是99.3%。98%是属于24的那一块里面的。

翟延昕 · 2022年03月05日

横轴是损失没错啊，面积才是概率啊，P(loss≤WCL）=98%，分位点取在44和24之间，根据谨慎性原则应取44才对啊

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