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LHY · 2020年10月17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.

还有最后这个expected loss (the mean ) = 40000 是怎么算出来的？

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2 个答案

袁园_品职助教 · 2020年10月19日

同学你好！

你可以再看一遍题目最后一句“ so $400,000 is the quantile at the 98% level of confidence or higher. Subtracting the mean gives $370,000. ”

这句话是说 400,000 是 worst case, 减去 expected loss 30,000，得到 credit VAR 370,000

EL = 30,000 是上一道题的答案，如果不明白的话可以去看下上一道题 PZ2016082406000007

袁园_品职助教 · 2020年10月18日

同学你好！

你说的“ expected loss (the mean ) = 40000 ” 是在哪里？

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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

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

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

2020-09-08 05:50 2 · 回答