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seven-zhu · 2022年10月08日

违约率

  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%（ 24+40）=32 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

如果两个Bond是independent的，那A违约B不违约的概率是不是就是 5% * （1-7%),在题目里面是用5% - 0.5%是因为两个Bond是有correlation的？

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已采纳答案

DD仔_品职助教 · 2022年10月09日

嗨，从没放弃的小努力你好：


如果说independent，B违约不违约跟A就没关系，A违约B不违约概率就是直接是A违约的概率=5%

具体同学可以看下面这张图：

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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