ARBITER: A Risk–Neutral Neural Operator for Arbitrage–Free SPX–VIX Term Structures

Battle Count: 50

Directly addresses SPX-VIX term structure modeling, which is central to equity derivatives trading, volatility trading, and risk management. The arbitrage-free guarantee, numéraire consistency, and VIX replication are critical for production derivatives systems. The operator-level approach replaces fragile post-hoc cleaning with in-training geometric constraints, reducing error accumulation under distribution shifts. Stress-to-Fail analysis and external validity protocols support deployment readiness. However, current evaluation is on synthetic data, and real-market validation is deferred.

Very high complexity: integrates selective state-space scans reinterpreted as Green operators, Q-Align Lipschitz projections with spectral normalization, CFL-style Spec-Guard with power iteration, convex-monotone ICNN decoder with Legendre duality, saddle-point extragradient training with two-time-scale updates, fixed stopping thresholds, HAC inference, Holm-Bonferroni correction, blocked cross-validation, and extensive logging/auditing infrastructure. Requires expertise in both financial mathematics (risk-neutral pricing, no-arbitrage constraints, VIX replication) and deep learning (SSMs, neural operators, constrained optimization).

Full code, configuration files, and scripts released. Single-command reproduction pipeline (make reproduce). Machine-independent recipe file (replicate.json) with fixed seeds, hardware descriptors, and environment specifications. All metrics, logs, and safety counters exported. Sweep ledger records configurations and random seeds for exact replay. Cross-validation ledger archives checkpoints, validation indices, and OOS boundaries. Artifact satisfies common reproducibility checklists.