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

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.