410140980 · 2023年07月20日

这道题的累积违约概率

NO.PZ2020033002000078

问题如下：

In a synthetic CDO, the homogeneous reference portfolio has following characters:

Number of reference entities = 50;

CDS spread, $s=180bp$ ;

Recovery rate $f=40\%$ .D

Defaults are independent.

The annual default probability on a single name is constant over five years and obeys the relation: $s={(1-f)}PD$ .

What is the expected number of defaulting entities over the next five years, and which of the following tranches would lose 100% of the principal invested and hence be entirely wiped out?

选项：

There would likely be 14 defaults and tranches up to the 3% are wiped.

There would likely be 14 defaults and tranches up to the 8.5% are wiped.

There would likely be 7 defaults and tranches up to the 3% are wiped.

There would likely be 7 defaults and tranches up to the 8.5% are wiped.

解释：

D is correct.

考点：CDO

解析：

先算 PD $d=\frac{1.8\%}{1-0.40}=3.00\%$ .

5年累积PD $d+S_1d+S_2d+S_3d+S_4d=3\%(1+0.970+0.941+0.913+0.885)=14.1\%$ ，where the survival rates are $S_1={(1-3\%)}=0.970$ , $S_2=S_1{(1-3\%)}=0.941$ , and so on.

The expected number of defaults is therefore $50\times14.1\%$ = 7.

With a recovery rate of 40%, the expected loss is 8.5% of the notional.

So, all the tranches up to the 8.5% point are wiped out.

老师这道题的题干当中的违约概率是怎么判断的呢？给的公式s=（1-f）*PD 不理解怎么解析算了五年的累积违约概率，这个解题思路是怎样的

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已采纳答案

DD仔_品职助教 · 2023年07月23日

嗨，从没放弃的小努力你好：

5年累计的PD是14.1%同时RR是40%，那么损失的期望就是14.1%*60%约等于8.5%

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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DD仔_品职助教 · 2023年07月22日

嗨，从没放弃的小努力你好：

同学你好，

根据题目给出的公式：s=(1−f)PD，可以反推出一年的PD=1.8%/(1-0.4)=3%

五年的累计违约概率就等于=第一年违约的概率+第一年没有违约*第二年违约了的概率+前一二年没有违约*第三年违约了的概率+前一二三年没有违约*第四年违约了的概率+前一二三四年没有违约*第五年违约了的概率

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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410140980 · 2023年07月23日

expected loss is 8.5% of the notional. 那这个8.5%怎么算来的

这道题的累积违约概率

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