# A Novel Approach to Quantification of Model Risk for Practitioners

## TL;DR

This paper introduces a mathematically rigorous framework for quantifying model risk in industry, using advanced concepts from differential geometry and functional analysis to address the complexity of modern models.

## Contribution

It proposes a novel approach that models model risk as a norm in a Banach space over a Riemannian manifold with Fisher--Rao metric, providing a comprehensive theoretical foundation.

## Key findings

- Framework covers data, mathematical foundations, infrastructure, and usage.
- Practitioners can identify relevant abstract concepts for risk quantification.
- The approach offers a general and sound mathematical basis for model risk assessment.

## Abstract

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.