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小猫批脸 · 2023年02月09日

看不懂 怎么和何老师上课讲的不一样

  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%. 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%

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

老师上课讲的 用的WCL直接就是ABC组合的portfolio 里面假如C违约了 那么loss直接就是C的exposure 然后WCL也就等于这个exposure 然后计算的Credit VaR


还是说这个exposure是题目直接给的 并不是按照EL算出来的？


我已经迷糊了 看不懂了

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DD仔_品职助教 · 2023年02月11日

嗨，从没放弃的小努力你好：


同学你好，

1，WCL的计算要根据分位点的概率来判断如何算，

老师在课上举的例子，C的违约概率刚好就是WCL的分位点概率，所以直接用这个loss来作为WCL。

而这个题是98%的WCL，AB的违约概率都是一个5%，一个7%，并且不是独立的，明显和98%不是一个分位点，所以我们要根据AB的违约情况，写出以下几种可能，来判断那一个数据是WCL：

A违约的loss=24m prob是4.5%

B违约的loss=20m prob是6.5%

概率计算如下图：

98%的WCL根据谨慎原则，应该选择24m。

2，这题关于EL没写清楚，具体的计算是：

EL A=60m*5%*（1-60%）=1.2m

EL B=40m*7%*（1-50%）=1.4m

总的EL就是他俩相加=2.6m


这道题是比较好的一到credit Var的计算，同学要好好掌握这道题，以本题的方法为准。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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