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Summer. · 2022年05月08日

joint default probability

  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 0.5% 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

提问 ， 为什么A default B no default 的概率是5%-0.5%？

我一开始是按5%*（1-7%）计算的， 后来又发现有一个default correlation =20%,

可是这些条件也算不出 P（A default B no default） = 5%-0.5%= 4.5%


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1 个答案

李坏_品职助教 · 2022年05月09日

嗨，从没放弃的小努力你好：


题干有一个信息：Give an assumption that the probability of joint default is 0.5% ，这个意思是A和B一起违约的概率只有0.5%，我们从A违约的概率里面扣掉A和B一起违约的0.5%，剩下的就是A违约B不违约的4.5%了。

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努力的时光都是限量版，加油！

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