Portfolio credit var

[Puneeta]

Hi david..
Could u help with the concept behind the non negative default correlation used in modelling credit risk...from the extract," we oftern set all the pairwise correlation equal to a single parameter"
That single parameter is market factor right??
And why it should be non negative and why non negative values disturb the matrix on default correlation...pls answer

 

[David Harper CFA FRM]

Hi @Puneeta I don't see the mathematical context but I am not aware of a restriction that the default correlation must be non-negative. Your first mention seems to refer to a default pairwise correlation matrix; e.g., if you have 10 credits in a portfolio, that's a 10*10 matrix where the diagonal in 1.0s (a credit is perfectly correlated to itself) with n*(n-1)/2 = 10*9/2 = 45 pairwise correlations. We might make a hugely simplifying assumption that they are all equal to the same parameter, but it can be negative. Alternatively, in the single-factor credit risk model (see Malz Chapter 8) there is an implicit assumption, I think, that the correlation (or Beta) bounds from zero to 1.0, but negative correlation (I think) is mathematically possible, as it would be a countercyclical credit: a credit whose conditional default probability decreases on an economic downturn (counterintuitive, yes?). It's hard to say what is meant by "disturb the matrix" without seeing the math. I'm not aware of a mathematical restriction ... there is just this practical idea, in the single factor model, that credits in general have positive exposure to the common factor. Sort of how we don't expect equity beta to be negative (right?) however it's mathematically entirely possible. I hope that's helpful,