Scenario Matching for Credit Dependence Stress Tests: Temporal correlation constraints and empirical risk bounds

Paper: arXiv 2610.35118

Authors: Naoufal Nifa

Abstract

We couple two sets of simulated market and credit paths by minimizing absolute temporal-correlation error relative to a prescribed target. Each market path receives exactly one credit path, preserving both empirical distributions of complete scenarios. A perfect-matching test identifies whether a uniform correlation-error tolerance is feasible and determines its smallest attainable value. Further assignments give exact empirical mean-loss and exceedance-probability bounds; quantile bounds follow by binary search over eligible loss thresholds. A synthetic bond-forward credit stress test illustrates the method. The experiments report matching precision, empirical score tails and exposure-grid error, and measure matching and mean-loss computation. The method is independent of the scenario generator and provides a reproducible way to examine dependence assumptions in existing risk engines. Tail measures concern default-probability-weighted credit scores. Accompanying reproducibility package (Python code, synthetic scenario libraries, permutations, and benchmarks) is attached in the ZIP archive.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sound approach to scenario matching using optimal transport and assignment problems. It demonstrates strong empirical rigor through a synthetic stress test, detailed numerical design, and analysis of matching precision and risk bounds. The methodology offers a novel way to examine dependence assumptions in existing risk engines, with a clear path to reproducibility.

Research Flowchart

  flowchart TD
    A[Research Goal: Reproducible Stress Test Dependence Assumptions] --> B{Key Methodology: Couple Market & Credit Paths};
    B -- Minimize --> C[Computational Process: Absolute Temporal-Correlation Error];
    C -- Inputs --> D(Data: Simulated Market Paths, Simulated Credit Paths);
    D -- Perfect Matching Test --> E{Outcomes: Smallest Attainable Uniform Correlation-Error Tolerance};
    E -- Further Assignments --> F[Outcomes: Exact Empirical Mean-Loss & Exceedance-Probability Bounds];
    F -- Illustration --> G(Synthetic Bond-Forward Credit Stress Test);
    G -- Analysis --> H[Key Findings: Matching Precision, Empirical Score Tails, Exposure-Grid Error, Method Performance];