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小猫批脸 · 2023年02月09日

最大的损失不应该是100嘛?

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

想问一下 同时违约的话 那不应该是 Probability loss(小于等于100)=99.5% 而Probability Loss(A=60)=95.5% 所以98%是夹在两个之间 那么谨慎性原则应该取100m?

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已采纳答案

品职答疑小助手雍 · 2023年02月09日

同学你好,首先违约概率的话,98%对应的应该是下图的位置:

然后损失的话,本题是有recovery rate的,所以A违约时候的损失不是60,而是60*40%=24M。

所以98%的wcl就是24M,减去EL2.6M 就得到credit var 21.4M。

小猫批脸 · 2023年02月10日

奥奥奥奥 明白了 是我想错了 是A违约的概率我不会计算 导致理解错了 所以说 那个违约概率的 老师能不能帮忙补充一下公式 就是 A违约B不违约的之类的 有咩有系统的公式讲解一下

小猫批脸 · 2023年04月26日

老师 这题 我怎么复习看不懂了 为什么A违约对应的损失是99.5? 不应该是95.5嘛?

品职答疑小助手雍 · 2023年04月27日

看表格,它是从下面开始累计起来的概率,累计到A违约B不违约那里是99.5%。

品职答疑小助手雍 · 2023年02月10日

这种概率用韦恩图表示比较清晰:

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