A Risk-Neutral Neural Operator for Arbitrage-Free SPX-VIX Term Structures
This addresses the problem of arbitrage-free interpolation and extrapolation in derivatives pricing for financial practitioners, though it is incremental as it builds on existing neural operator methods with specific constraints.
The paper tackled the problem of learning joint SPX-VIX term structures under no-arbitrage constraints by proposing ARBITER, a risk-neutral neural operator that enforces static arbitrage bounds and monotonicity, showing gains over Fourier Neural Operator, DeepONet, and state-space models on historical data with metrics like reduced Dual-Gap and improved NI.
We propose ARBITER, a risk-neutral neural operator for learning joint SPX-VIX term structures under no-arbitrage constraints. ARBITER maps market states to an operator that outputs implied volatility and variance curves while enforcing static arbitrage (calendar, vertical, butterfly), Lipschitz bounds, and monotonicity. The model couples operator learning with constrained decoders and is trained with extragradient-style updates plus projection. We introduce evaluation metrics for derivatives term structures (NAS, CNAS, NI, Dual-Gap, Stability Rate) and show gains over Fourier Neural Operator, DeepONet, and state-space sequence models on historical SPX and VIX data. Ablation studies indicate that tying the SPX and VIX legs reduces Dual-Gap and improves NI, Lipschitz projection stabilizes calibration, and selective state updates improve long-horizon generalization. We provide identifiability and approximation results and describe practical recipes for arbitrage-free interpolation and extrapolation across maturities and strikes.