  Models continue to increase their already broad use across industry as well
as their sophistication. Worldwide regulation oblige financial institutions to
manage and address model risk with the same severity as any other type of risk,
which besides defines model risk as the potential for adverse consequences from
decisions based on incorrect and misused model outputs and reports. Model risk
quantification is essential not only in meeting these requirements but for
institution's basic internal operative. It is however a complex task as any
comprehensive quantification methodology should at least consider the data used
for building the model, its mathematical foundations, the IT infrastructure,
overall performance and (most importantly) usage. Besides, the current amount
of models and different mathematical modelling techniques is overwhelming.
  Our proposal is to define quantification of model risk as a calculation of
the norm of some appropriate function that belongs to a Banach space, defined
over a weighted Riemannian manifold endowed with the Fisher--Rao metric. The
aim of the present contribution is twofold: Introduce a sufficiently general
and sound mathematical framework to cover the aforementioned points and
illustrate how a practitioner may identify the relevant abstract concepts and
put them to work.
