If A and B be two debt securities, which of the following is true?

If the marginal probability of default of two securities A and B is P(A) and P(B), then the probability of

both of them defaulting together is affected by the default correlation between them. Marginal

probability of default means the probability of default of each security on a standalone basis, ie, the

probability of default of one security without considering the other security.

The relationship that expresses the probability of joint default of the two is given by the following

expression:

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It is easy to see that in a situation where the Default Correlation of A & B = 0, ie, the defaults are

independent, the combined probability of default is P(A)*P(B), exactly what we would intuitively

expect. Also in the other extreme case where the default correlation is equal to 1 and P(A) = P(B) = p,

ie the securities behave in an identical way, the expression resolves to just p, which is what we would

expect.

From the above relationship, it is clear that the probability of joint default of A and B is the greatest

when default correlation between the two is equal to 1, ie the securities behave in an identical way.

Therefore Choice 'a' is the correct answer.