Paper: arXiv 2506.13435

Authors: Nan Guo, Ruodu Wang, Chenxi Xia, Jingping Yang

Abstract

Credit ratings are widely used by investors as a screening device. We introduce and study several natural notions of risk consistency that promote prudent investment decisions in the framework of Choquet rating criteria. Three closely related notions of risk consistency are considered: with respect to risk aversion, the asset pooling effect, and the benefit of portfolio diversification. These notions are formulated either under a single probability measure or multiple probability measures. We show how these properties translate between rating criteria and the corresponding risk measures, and establish a hierarchical structure among them. These findings lead to a full characterization of Choquet risk measures and Choquet rating criteria satisfying risk consistency properties. Illustrated by case studies on collateralized loan obligations and catastrophe bonds, some classes of Choquet rating criteria serve as useful alternatives to the probability of default and expected loss criteria used in practice for rating financial products.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous axiomatic mathematical characterization of Choquet rating criteria and risk consistency properties. It bridges quantitative risk management theory and credit rating practice, supported by theoretical proofs and initial case studies on CLOs and catastrophe bonds.

Research Flowchart

  flowchart TD
    A[Research Goal: Evaluate & Improve Risk Consistency in Choquet Credit Ratings] --> B[Formulate Risk Consistency Notions: Risk Aversion, Pooling, & Diversification]
    B --> C[Translate Properties Between Rating Criteria & Choquet Risk Measures]
    C --> D[Establish Hierarchical Structure & Full Characterization of Measures]
    D --> E[Inputs & Case Studies: Structured Products CLOs & Catastrophe Bonds]
    E --> F[Key Outcomes: Unified Framework & Better Alternatives to Probability of Default/Expected Loss]