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王垚 · 2020年09月08日

问一道题：NO.PZ2016082406000008

  1. FRM II
  2. Credit Risk Measurement And Management

问题如下：

A portfolio consists of two bonds. The credit VAR is defined as the maximum loss due to defaults at a confidence level of 98% over a one-year horizon. The probability of joint default of the two bonds is 1.27%, and the default correlation is 30%. The bond value, default probability, and recovery rate are USD 1,000,000, 3%, and 60% for one bond, and USD 600,000, 5%, and 40% for the other. what is the best estimate of the unexpected credit loss (away from the ECL), or credit VAR, for this portfolio?

选项：

A.

USD 570,000

B.

USD 400,000

C.

USD 360,000

D.

USD 370,000

解释：

ANSWER: D

Here, the joint default probability matters. If the two bonds default, the loss is$1,000,000×(1−60%)+$600,000×(1−40%)=$400,000+$360,000=$760,000\$1,000,000\times\left(1-60\%\right)+\$600,000\times\left(1-40\%\right)=\$400,000+\$360,000=\$760,000.

This will happen with probability 1.27%. The next biggest loss is $400,000, which has probability of 3.00%-1.27%=1.73%

Its cumulative probability must be 100.00−1.27=98.73%100.00-1.27=98.73\%. This is slightly above 98%, so $400,000 is the quantile at the 98% level of confidence or higher. Subtracting the mean gives $370,000.

选%的时候，不是应该选择大一点的么？为什么不能选择760的98.7%呢？为什么还需要再算一个400的loss呢？谢谢

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2 个答案

小刘_品职助教 · 2020年09月19日

同学你好，

这个概率不是问发生的概率，而是问损失小于760的概率。

两个债券同时违约之后，最大的损失就760，所以不可能有违约金额超过760了，反过来说，也就是P（违约金额<=760000）=100% 

小刘_品职助教 · 2020年09月08日

同学你好，

这道题取略大的就行。

760对应的概率是100%，而不是98.7%。

第一大违约金额是760000，P（违约金额<=760000）=100% 

第二大违约金额是400000  P（违约金额<=400000）=98.73%

按照98%的置信水平取违约金额是400000已经是谨慎性原则了。

vivian_zm · 2020年09月19日

为什么760对应的概率是100%，而不是98.7%？joint probability of default不是1.27%吗

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US400,000 US360,000 US370,000 ANSWER: Here, the joint fault probability matters. If the two bon fault, the loss is $1,000,000×(1−60%)+$600,000×(1−40%)=$400,000+$360,000=$760,000\$1,000,000\times\left(1-60\%\right)+\$600,000\times\left(1-40\%\right)=\$400,000+\$360,000=\$760,000$1,000,000×(1−60%)+$600,000×(1−40%)=$400,000+$360,000=$760,000. This will happen with probability 1.27%. The next biggest loss is $400,000, whihprobability of 3.00%-1.27%=1.73% Its cumulative probability must 100.00−1.27=98.73%100.00-1.27=98.73\%100.00−1.27=98.73%. This is slightly above 98%, so $400,000 is the quantile the 98% level of confinor higher. Subtracting the megives $370,000. ​请问第二大损失400000发生的概率是如何推导的？

2021-02-01 14:48 1 · 回答

还有最后这个expecteloss (the me) = 40000 是怎么算出来的？

2020-10-17 09:54 2 · 回答

为什么算expecteloss的时候 只考虑回收率而不考虑 fault probability呢？

2020-10-17 09:51 1 · 回答

The next biggest loss is $400,000, whihprobability of 3.00%-1.27%=1.73% 请问为什么概率不是3%*（1-5%）=2.85%

2020-09-19 11:49 3 · 回答