Beta and Kernel Distribution

[peter333]

Dear David :

I have two questions on De Servigny Chapter 4 on loss given default. May be you can help

(1) You say that Kernel modeling is nonparametric technique. So I think it should not be based on some distribution and just from sample, we should make inference. But you write at the same time that it uses Gaussian PDF for inferring probabilities. I could not get it.

(2) In beta distribution, you said that as standard deviations are large so we must use stochastic recovery rate. Why the presence of large standard erros would make this randomness necessary for recovery rates?

best wishes

Peter

 

[David Harper CFA FRM]

Hi Peter

(1) It has a parametric element but is overall non parametric (wiki is pretty good). Non parametric because it's basically a histogram but where observations are not equally weighted and the normal (Gaussian) *could* be "kernel" function that is used to apply the weights. Main job: to use a histogram but be able to "plug the holes" in the actual observations

(2) I think you have a arguable idea there, interesting. I just parrot de Servigny where his point is: large standard deviations imply we cannot very much use a constant or unconditional mean recovery/LGD. I fetched this from the creditmetrics tech doc which I think makes the point nicely:

"Recovery rates are best characterized, not by the predictability of their mean, but by their consistently wide uncertainty. Loss rates are bounded between 0% and 100% of the amount exposed. If we did not know anything about recovery rate, that is, if we thought that all possible recovery rates were equally likely, then we would model them as a flat (i.e., uniform) distribution between the interval 0 to 1. Uniform distributions have a mean of 0.5 and a standard deviation of 0.29 ( ). The standard deviations of 25.45% for senior unsecured bonds and 32.7% for bank facilities are on either side of this and so represent relatively high uncertainties.

We can capture this wide uncertainty and the general shape of the recovery rate distribution – while staying within the bounds of 0% to 100% – by utilizing a beta distribution. Beta distributions are flexible as to their shape and can be fully specified by stating the desired mean and standard deviation." (p 80)."

Do you think adding "key points," as below, is helpful?

Key points (for FRM):

* Recovery/LGD are notoriously hard to parameterize; data shows wide dispersion
* Empirically, most LGD models perform poorly
* Beta distribution often used (Portfolio Manager, PRT, CreditMetrics) primarily due to flexibility (takes many shapes) but cannot be binomal (two humped) which are observed
* Kernel modeling is non parameteric alternative

 

[peter333]

Thanks David...your answer is quite helpfull and especially the referenced article is very useful and interesting

best regards,
peter