An axiomatic approach to default risk and model uncertainty in rating systems

Paper: arXiv 2303.08217

Authors: Max Nendel, Jan Streicher

Abstract

In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We discuss different properties and representations of default risk measures via monetary risk measures, families of related tail risk measures, and Choquet capacities. In a second step, we turn our focus on default risk measures, which are given as worst-case PDs and distorted PDs. The latter are frequently used in order to take into account model risk for the computation of capital requirements through risk-weighted assets (RWAs), as demanded by the Capital Requirement Regulation (CRR). In this context, we discuss the impact of different default risk measures and margins of conservatism on the amount of risk-weighted assets.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical framework, extending probability of default via Choquet capacities and monetary risk measures to handle model uncertainty. While strong in theoretical formulation and regulatory policy analysis (CRR/RWA), it lacks real-world empirical validation or datasets.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Axiomatize Default Risk & Model Risk<br>in Credit Rating Systems"] --> B["Framework Formulation:<br>Define Default Risk Measures via<br>Monetary Measures & Choquet Capacities"]
    C["Inputs & Regulatory Rules:<br>Capital Requirements Regulation (CRR)<br>& Baseline Probability of Default (PD) Models"] --> D["Computational Analysis:<br>Calculate Risk-Weighted Assets (RWAs)<br>using Worst-Case & Distorted PDs"]
    B --> D
    D --> E["Findings & Outcomes:<br>Quantified impact of Margins of Conservatism<br>and Model Uncertainty on RWA Capital"]