# Model Risk in Credit Risk

## TL;DR

This paper rigorously characterizes all possible default models within exchangeable Bernoulli sequences and assesses how model risk impacts portfolio loss measures like VaR and Expected Shortfall.

## Contribution

It provides an analytical description of all joint default models in a specific class and quantifies the impact of model risk on loss metrics.

## Key findings

- Model risk significantly affects VaR and ES estimates.
- All possible joint default models are characterized analytically.
- Quantitative measures of model risk impact are provided.

## Abstract

The issue of model risk in default modeling has been known since inception of the Academic literature in the field. However, a rigorous treatment requires a description of all the possible models, and a measure of the distance between a single model and the alternatives, consistent with the applications. This is the purpose of the current paper. We first analytically describe all possible joint models for default, in the class of finite sequences of exchangeable Bernoulli random variables. We then measure how the model risk of choosing or calibrating one of them affects the portfolio loss from default, using two popular and economically sensible metrics, Value-at-Risk (VaR) and Expected Shortfall (ES).