If the probability of the two bonds defaulting simultaneously is 1.4%, what is the default correlation between the two?

There are two bonds in a portfolio, each with a market value of $50m. The probability of default of the two bonds are 0.03 and 0.08 respectively, over a one year horizon.

If the probability of the two bonds defaulting simultaneously is 1.4%, what is the default correlation between the two?
A . 0%
B . 100%
C . 40%
D . 25%

Answer: D

Explanation:

Probability of the joint default of both A and B =

We know all the numbers except default correlation, and we can solve for it. Default Correlation*SQRT(0.03*(1 – 0.03)*0.08*(1 – 0.08)) + 0.03*0.08 = 0.014. Solving, we get default correlation = 25%