开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)|3.2.5(安卓)APP下载

Sarah · 2021年02月01日

问一道题:NO.PZ2016082406000008 [ FRM II ]

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×(160%)+$600,000×(140%)=$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 100.001.27=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.

​请问第二大损失400000发生的概率是如何推导的?

1 个答案
已采纳答案

小刘_品职助教 · 2021年02月01日

同学你好,

这个概率直接画文氏图就可以,债券A违约的概率是3%,A和B同时违约的概率是1.27%,那A违约B不违约的概率就是3-1.27%=2.73%