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良爱洳 · 2021年11月14日

问一道题:NO.PZ2020033002000008 [ FRM II ]

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?
1 个答案
已采纳答案

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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