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nanaluo · 2022年10月30日

请问题目条件

NO.PZ2020033002000010

问题如下:

Assume that the one-year probabilities of default for the AAA- and BBB-rated bonds are 1% and 4%, respectively, and the joint probability of default of the two bonds is 0.07%. What is the default correlation between the two bonds?

选项:

A.

0.03%

B.

1.54%

C.

78.91%

D.

The default correlation cannot be calculated with the information provided.

解释:

B is correct.

考点:Default Correlation

解析:

From Equation: p(A and B)=Corr(A,B)p(A)[1p(A)]×p(B)[1p(B)]+p(A)p(B)p{(\text{A and B})}=Corr{(\text{A,B})}\sqrt{p{(\text{A})}{\lbrack1-p{(\text{A})}\rbrack}}\times\sqrt{p{(\text{B})}{\lbrack1-p{(\text{B})}\rbrack}}+p{(\text{A})}p{(\text{B})} , the default correlation is Corr(A,B)=p(A and B)p(A)p(B)p(A)[1p(A)]×p(B)[1p(B)]Corr{(\text{A,B})}=\frac{p{(\text{A and B})}-p{(\text{A})}p{(\text{B})}}{\sqrt{p{(\text{A})}{\lbrack1-p{(\text{A})}\rbrack}}\times\sqrt{p{(\text{B})}{\lbrack1-p{(\text{B})}\rbrack}}}=0.00070.01×0.040.01×(10.01)0.04×(10.04)=0.0154=\frac{0.0007-0.01\times0.04}{\sqrt{0.01\times(1-0.01)}\sqrt{0.04\times(1-0.04)}}=0.0154.

题目是否还需要说明 AAA- and BBB-rated bonds的违约概率均满足Bernoulli分布?

1 个答案

DD仔_品职助教 · 2022年10月30日

嗨,爱思考的PZer你好:


我觉得,精确来讲,如果想要用到下面的公式,是需要说个前提条件的,但是这里出题吧,出题人都是FRM考过试的持证人,一般不会像CFA一样把题目出的完美无缺,条件全部都给齐的,所以我们做题也就只能将就一下了。。。出到哪里就用哪里的公式好了。

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