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良爱洳 · 2021年11月14日

问一道题：NO.PZ2020033002000008 [ FRM II ]

  1. FRM II
  2. Credit Risk Measurement And Management

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

请问wcl＝24是怎么算出来的？
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品职答疑小助手雍 · 2021年11月14日

同学你好，

AB同时违约的概率是0.7%，损失是44m。占据损失最大的尾部的0.7%。前面累计概率99.3%。

A违约但是B不违约的概率是5%-0.7%=4.3%，占据了损失第二大的部分，占据的累计概率是95%到99.3%的部分，包含了98%，所以98%的wcl就是24。

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