请问题目条件

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: $p{(\text{A and B})}=Corr{(\text{A,B})}\sqrt{p{(\text{A})}{\lbrack1-p{(\text{A})}\rbrack}}\times\sqrt{p{(\text{B})}{\lbrack1-p{(\text{B})}\rbrack}}+p{(\text{A})}p{(\text{B})}$ , the default correlation is $Corr{(\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}}}$$=\frac{0.0007-0.01\times0.04}{\sqrt{0.01\times(1-0.01)}\sqrt{0.04\times(1-0.04)}}=0.0154$.