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Catherine · 2023年07月28日

五年累计违约概率

  1. FRM II
  2. Credit Risk Measurement And Management

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=180bps=180bp;

Recovery rate f=40%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)PDs={(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：

A.

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

B.

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

C.

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

D.

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=1.8%1−0.40=3.00%d=\frac{1.8\%}{1-0.40}=3.00\%.

5年累积PD d+S1d+S2d+S3d+S4d=3%(1+0.970+0.941+0.913+0.885)=14.1%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 S1=(1−3%)=0.970S_1={(1-3\%)}=0.970, S2=S1(1−3%)=0.941S_2=S_1{(1-3\%)}=0.941, and so on.

The expected number of defaults is therefore 50×14.1%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.

为什么不能用1-e的（-lambda×t）

t代入5

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1 个答案

李坏_品职助教 · 2023年07月28日

嗨，努力学习的PZer你好：


你说的那种是给出了hazard rate再去求某个债券在一段时间的累计违约概率。


这道题是给出了每年的PD，去计算有多少个债券违约，每个债券之间都是独立不相关的，而不是去算一个债券的累计违约概率，和1-exp(-λt)公式场景不匹配。

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NO.PZ2020033002000078问题如下 In a synthetic C, the homogeneous referenportfolio hfollowing characters:Number of referenentities = 50; C sprea s=180bps=180bps=180bp; Recovery rate f=40%f=40\%f=40%.efaults are inpennt. The annufault probability on a single name is constant over five years anobeys the relation: s=(1−f)P={(1-f)}P=(1−f)P Whis the expectenumber of faulting entities over the next five years, anwhiof the following tranches woullose 100% of the principinvesteanhenentirely wipeout? A.There woullikely 14 faults antranches up to the 3% are wipeB.There woullikely 14 faults antranches up to the 8.5% are wipeC.There woullikely 7 faults antranches up to the 3% are wipeThere woullikely 7 faults antranches up to the 8.5% are wipe is correct.考点C解析先算 P1.8%1−0.40=3.00%\frac{1.8\%}{1-0.40}=3.00\%1−0.401.8%​=3.00%. 5年累积PS1S2S3S43%(1+0.970+0.941+0.913+0.885)=14.1%S_1S_2S_3S_43\%(1+0.970+0.941+0.913+0.885)=14.1\%S1​S2​S3​S4​3%(1+0.970+0.941+0.913+0.885)=14.1%，where the survivrates are S1=(1−3%)=0.970S_1={(1-3\%)}=0.970S1​=(1−3%)=0.970, S2=S1(1−3%)=0.941S_2=S_1{(1-3\%)}=0.941S2​=S1​(1−3%)=0.941, anso on. The expectenumber of faults is therefore 50×14.1%50\times14.1\%50×14.1% = 7. With a recovery rate of 40%, the expecteloss is 8.5% of the notional. So, all the tranches up to the 8.5% point are wipeout. 烦请详细说下这题在说什么？数字啥意思？问题是啥意思？谢谢，完全读不懂。

2023-09-21 19:43 2 · 回答

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