First to default swap

[higaurav]

Hi David,

I need your help in understanding that why correlation in the underlying credit (in the swap basket) and the swap pricing are inversely related. I thought highly correlated asset will be a riskier proposition and therefore the spread should be higher whereas in the explanation it is given otherwise with the reason that it is easy to assess the single risk factor in this case. Require your help in understanding this. Pls help.

Rgrds,
OM

 

[David Harper CFA FRM]

Hi OM,

Please look at same question from earlier in the year here.
(It includes a link to this post)
I do not follow the "reason that it is easy to assess the single risk factor in this case"

Traditionally, we can understand it with the binomial example that I show; e.g., assume 100 credits with PD of 5% each. If independent (rho = 0), odds of triggering a "first to default" (note difference from high n-to-default!), are about 99%+ (1 - 95%^100). Now increase correlation to rho = 1, and odds of triggering a 1st-to-default go DOWN to only 5%.

It is maybe counterintuive, but key is: which n in n-to-default are we talking about (jr tranche? sr tranche) and then seeing that lower correlation is creating a distribution with fatter tails

David

 

[phwdisse]

Dear David,

I do understand this with correlation 1 or 0. But wat happens if there is a negatief correlation.

There is a question 31 in practice exam 2008 II

Kind Regards,

Paul

 

[David Harper CFA FRM]

Paul,

I consider the question to #31 un-answerable, and the answer to be totally incorrect. The mezzanine tranche is ambivalently responding to underlying default correlation (there is an answer but it results from complexity). The answer really surprises me as the ambivalence of the mezzanine is well known. Also, (a) and (b) are too alike.

In regard to the junior tranche, negative (default) correlation continues the trend observed from rho = 1.0 (odds of 1st-to-default PD low) to 0.0 (high or higher) to -1.0 (certain). Imagine the wholly unrealistic scenario:

* two assets
* default correlation = -1.0
* 1st to default (i.e., junior tranche equivalent)

under these assumptions, there must be a default!

David