A Certified Higher Order Quantum Framework for CSA and Margin-Aware Collateral Optimization

Abstract: Collateral allocation for uncleared derivatives is a legally constrained and operationally discrete optimization problem. Institutions must satisfy margin requirements while respecting CSA eligibility rules, valuation percentages, rounding, transfer thresholds, concentration limits, custody conditions, inventory, and VM, IM, or IA side constraints. This manuscript develops CR-HO-QAOA, a certified higher-order quantum candidate-generation framework for margin- and CSA-aware collateral allocation. The framework is adapter-first: official SIMM, proxy SIMM, legacy IA, VM-only, RQV, or hybrid margin sources are normalized into a common MarginRequirement, so the optimizer does not calculate or replace official SIMM. Given the requirement, CSA terms, and inventory, the optimizer builds a bounded active neighborhood of pledge, recall, substitution, batch, and slack actions. These actions define a higher-order binary model whose hyperedges capture concentration pressure, custody batches, substitution tickets, chunky lots, liquidity effects, overshoot, and side-specific requirements. The quantum layer maps hyperedges into a Pauli-Z cost Hamiltonian and uses collateral-specific feasible-subspace mixers to preserve one-hot choices, movement budgets, side assignments, and substitution structure. Candidates are decoded, repaired if needed, evaluated under an eight-term production objective, and certified by a deterministic CP-SAT master solver before any recommendation is reported. Synthetic benchmarks show that higher-order, constraint-preserving candidate generation can improve certified sample quality relative to QUBO-style and generic-mixer baselines, while CP-SAT remains the feasibility and governance arbiter. These results are synthetic workflow-validation evidence only, not evidence of hardware quantum advantage or production bank savings.