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天天 · 2023年07月13日

98%的WCL应该比95.5%的损失24更大才对吧？为什么取了个小数值的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%. Give an assumption that the probability of joint default is 0.5% 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 0.5%

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

98%的WCL应该比95.5%的损失24更大才对吧？为什么取了个小数值的24？

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2 个答案

pzqa27 · 2023年09月11日

嗨，努力学习的PZer你好：


这种题目最好不要倒推，就正着推累积损失，这样也好想。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

pzqa27 · 2023年07月14日

嗨，从没放弃的小努力你好：


您的算法是有问题的，损失分布是个累积的过程，不是1-4.5%=95.5%就得出了，具体算法如下

当没有损失的时候，发生概率是88.5%（100-7-5+0.5）

然后是当B发生违约时的，累积的概率是88.5%+6.5%=95%

然后是当A发生违约B不违约，累积的概率是95%+4.5%=99.5%，已经超过我们要求的98%，所以WCL根据保守原则选这个

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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！

罗小惠🌟 · 2023年09月09日

能够理解老师这里的思路，就是视频中例题第一个正推累计可能性的思路，但是能不能麻烦老师像何老师一样采用一下倒退的思路讲解一下呢？就是从A和B都违约（也就是最大损失），然后往前推。我自己尝试一下感觉不太能够得到同样的结论。

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