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𝒜𝒩𝒥𝒜 安雅🎃 · 2023年09月03日

计算credit VaR的两种式子，何时该用哪一个？

  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

计算Credit VaR（也就是UL）有两个式子，如下：



为什么这题是用第一个WCL-ECL，而不是用第二个式子？明明题干也给出能够计算出UL1和UL2的条件了。

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品职答疑小助手雍 · 2023年09月03日

同学你好，这题给了default correlation但是其实没啥用，recovery rate也不一样，还是得不到UL的相关系数。

一般这种只给了2个债券的题，都是要算各种损失情况以及对应的概率，然后累计概率排序求WCL，然后减EL得到credit var的。

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