问一道题：NO.PZ2016082406000007

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 expected credit loss of the portfolio?

选项：

USD 0

USD 9,652

USD 20,348

USD 30,000

解释：

ANSWER: D

The ECL is for the first bond $1,000,000\times3\%\times{(1-60\%)}=12,000$ , and for the second $600,000\times5\%\times{(1-40\%)}=18,000$ . This adds up to $30,000. Note that this number does not depend on the default correlation.

这一题用joint probability应该怎么求？

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小刘_品职助教 · 2020年10月23日

同学你好，

这道题不需要用到joint probability，如果非要用的话，结果也是一样的，如下所示：

（1）若X违约，则损失为1*40%=0.4m

（2）若Y违约，则损失为0.6*60%=0.36m

接下来算ECL，

（1）仅X违约，Y不违约概率为3%-1.27%=1.73%，损失为1.73%*0.4m=6920

（2）仅Y违约，X不违约概率为5%-1.27%=3.73%，损失为3.73%*0.36m=13428

（3）X、Y同时违约，概率为1.27%，损失为1.27%*(0.4+0.36)m=9652

ECL=6920+13428+9652=30000

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A portfolio consists of two bon. The cret Vis finethe maximum loss e to faults a confinlevel of 98% over a one-yehorizon. The probability of joint fault of the two bon is 1.27%, anthe fault correlation is 30%. The bonvalue, fault probability, anrecovery rate are US1,000,000, 3%, an60% for one bon anUS600,000, 5%, an40% for the other. Whis the expectecret loss of the portfolio? US0 US9,652 US20,348 US30,000 ANSWER: The Eis for the first bon1,000,000×3%×(1−60%)=12,0001,000,000\times3\%\times{(1-60\%)}=12,0001,000,000×3%×(1−60%)=12,000, anfor the secon600,000×5%×(1−40%)=18,000600,000\times5\%\times{(1-40\%)}=18,000600,000×5%×(1−40%)=18,000. This as up to $30,000. Note ththis number es not penon the fault correlation. 老师，为什么不用考虑相关性呢？这个给了joint fault probability，能用这个参数去计算么？

2020-03-21 12:22 2 · 回答

问一道题：NO.PZ2016082406000007

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