hi group,
thanks to Glen and Jon, and sorry in case I did not express myself clearly.
What I want to model are recovery rates, defined as (costs and earnings at
default)/(contract value). That is, there are two or more factors, or RVs,
in the numerator which are summed up, and one in the denominator. The
question then was whether to model numerator and denominator separately, and
if not how to model the ratio(s). And all that assuming that the RVs in the
numerator are not independent of that in the denominator (e.g. the reselling
value should be higher when the contract value is higher).
As it seems, there is no tractable solution for an explicit modeling of each
of the RVs, so most likely I will return to the beta.
Sincerely,
Alexander Hener.
Alexander Hener schrieb:
> hi group,
>
> I have a modelling problem where any help would be appreciated.
> Assume that I want to model a fraction, where the nominator is a sum of,
> say, four continous random variables. I am thinking of using some
> parameter-additive distribution there, e.g. the gamma, since the sum in
> the nominator needs not be negative. The denominator should be continous
> and positive. Now my questions are :
>
> 1. Is anyone aware of distributions which lend themselves to such a
> model ?
>
> 2. To make things just a little bit more complicated, the (in this case
> four) nominator random variables should be dependent on each other only
> by the nominator. Does anyone know about results for the divisioning of
> dependent variables which I could use in this case?
>
> Thanks in advance,
>
> Alexander Hener.
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