 # default swap

Dear Alll:

According to the problem below, why is it that the default correlation are lower?

Thank yoo so much for your time

Which of the following most accurately describes the pricing of a first-to-default basket of credit default swaps in a correlation trade? The swap premium will be higher when the number of credit default swaps is:

A) higher and when the default correlations are lower. B) higher and when the default correlations are higher. C) lower and when the default correlations are higher.

If correlations are lower, there are more scenarios where at least one default happens. To illustrate, let’s say your basket has two securities, and default probability for each security is 50%. Let’s say condition 1 is no default and condition 0 is a default.

If correlation is 1 (highest possible correlation/perfect correlation), the scenarios are:

{0, 0} and {1, 1}, each with 50% probability. Probability of at least one default is 50%.

If correlation is 0 (completely independent), the scenarios are:

{0, 0}, {0, 1}, {1, 0}, {1, 1}, each with 25% probability. Probability of at least one default is 75%.

If correlation is -1, the scenarios are:

{1, 0} and {0, 1}. Probability of default is 100%

So as you can see from this example, if correlation is high, there are more “blank” scenarios where no default happens. If correlation decreases to zero, at least one security can fall into a default scenario even if other securities don’t default. If correlation is negative, a non-default in some securities makes a default in other securities more likely.