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ysr1990 · 2020年11月09日

问一道题:NO.PZ2016082406000078

问题如下:

Consider the following homogeneous reference portfolio in a synthetic CDO: number of reference entities, 100; CDS spread, s=150bps=150bp; recovery rate f=50%f=50\%. Assume that defaults are independent. On a single name the annual default probability 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 be entirely wiped out (lose 100% of the principal invested) by the expected number of defaulting entities?

选项:

A.

There would likely be 14 defaults and a [3%—14%] tranche would be wiped out.

B.

There would likely be 3 defaults and a [0%—l%] tranche would be wiped out.

C.

There would likely be 7 defaults and a [2 %—3%] tranche would be wiped out.

D.

There would likely be 14 defaults and a [6%—7%] tranche would be wiped out.

解释:

ANSWER: D

The annual marginal PD is d=1.5%10.50=3.00%d=\frac{1.5\%}{1-0.50}=3.00\%. Hence the cumulative PD for the five years is 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 100×14.1%100\times14.1\%, or 14. With a recovery rate of 50%, the expected loss is 7% of the notional. So, all the tranches up to the 7% point are wiped out.

这道题到底是啥意思呢,没读懂

1 个答案

品职答疑小助手雍 · 2020年11月09日

嗨,从没放弃的小努力你好:


其实就是按照题目给的spread=(1-f)*PD往下一步一步算。

先通过spread和LGD算出来PD,3%

然后求累计5年的PD,第一年违约的概率+1不违约2违约的概率+……+1-4不违约5违约的概率,14.1%

所以期望的违约率就是14.1%,在乘以个数100,就等于期望的违约个数:14。

因为rr是50%,所以PD*LGD得到期望的总损失大概是6-7%。(这些会被wiped out)


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