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Catherine · 2023年07月28日

五年累计违约概率

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=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=(1f)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%10.40=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=(13%)=0.970S_1={(1-3\%)}=0.970, S2=S1(13%)=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

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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2023-09-21 19:43 2 · 回答

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