Derivative-Informed Operator Learning for Finance: On-the-Fly Greeks, Surfaces, Hedging, and Control

Battle Count: 50

Highly relevant to quantitative trading and financial engineering. The paper directly addresses the core need for fast, accurate, and differentiable pricing surrogates that produce not just prices but Greeks, sensitivities, and risk measures essential for hedging, portfolio optimization, XVA, and stress testing. The derivative-informed framework is specifically designed for financial decision systems where downstream tasks depend on derivatives (deltas, vegas, curve sensitivities, exposure gradients). The hedging error bounds (Theorems 2-3) and optimizer stability results (Theorem 4) are directly applicable to trading desk operations. The paper bridges neural operator learning with practical financial engineering needs including calibration, risk management, and control. However, it remains at the mechanism/validation stage rather than production deployment.

Moderate to high complexity. The framework requires: (1) access to a high-fidelity pricing/risk engine capable of generating derivative actions (tangent PDEs, adjoint PDEs, AAD, pathwise Monte Carlo, implicit differentiation); (2) neural operator architectures (DeepONet, FNO, or random-feature operators); (3) careful loss scaling across heterogeneous derivative quantities (prices, deltas, vegas, PV01s have different units); (4) economically meaningful derivative direction sampling (PCA factors, stress modes, key-rate bumps); (5) no-arbitrage constraint implementation; (6) multi-dimensional validation protocol. The random-feature experiments are simpler (single ridge solve), but the full operator-level framework with on-the-fly derivative generation, random sketching, and economic constraints requires significant engineering. The paper provides pseudocode (Appendix D) and implementation details (Section 10) but production deployment would require substantial additional work.

The paper provides three reproducible experiments with multi-seed (8 seeds) results, explicit hyperparameters (derivative weight λ, network architecture, optimizer settings), and accompanying scripts. Finite-difference consistency checks, quadrature sanity checks, and no-arbitrage diagnostics are included. However, the experiments are controlled benchmarks (Black-Scholes slice, random-feature surrogates, stylized curve-to-surface operator) rather than market-scale deployments. The paper explicitly states these are mechanism demonstrations, not production benchmarks. Code is referenced as accompanying the paper but no explicit GitHub URL is provided in the extract.