Fitting distribution to a given data

Question

I have a loss data arising out of Operation risk for some particular bank. The standard procedure for arriving at the capital charge w.r.t. Operational risk needs I fit some continuous distribution to this loss data.

Normally, I am able to fit some standard distributions. Once the distribution is identified, the same distribution is used to simulate future loss amounts.

My question is assuming the data is such that I am just not able to fit any statistical distribution, how do I deal with data to simulate the loss amounts. Is there any non-parametric method available to deal with such situations.

Kindly give me some advice.

Answer 1

You could resample the observed data (bootstrapping).

The problem with that is the real risk is in the extreme tail... and the sample doesn't really give you any information there (e.g. if you're interested in say a tail value at risk, for $\alpha = 0.005$ but you only have a couple of hundred observations, then you have no information about the behavior of the tail out that far.

On the other hand if you had many thousands of observations it may not be a big problem.

You may get better benefit from investigating extreme value distributions (which do deal with the extreme tail), but that's not quite nonparametric.

Answer 2

in banking you have to use also the external data. the regulators will insist that you don't come up with distribution strictly on your own dataset. so this becomes rather complicated. for instance take a look at change of measure approach. the paper also discusses the scenarios - another part of oprisk estimation.