Amortizing the Calibration Triple: A Projection-Consistent Neural Operator for Local-Stochastic Volatility

Battle Count: 51

Highly relevant to quantitative trading desks dealing with exotic derivatives, LSV model calibration, and real-time risk management. The 164x speedup in calibration latency (98.5ms to 0.6ms) directly impacts intraday pricing and hedging workflows. The projection-consistent triple ensures internal model coherence for exotic pricing engines. However, the method is primarily a calibration/pricing infrastructure tool rather than a direct trading signal generator. Relevance is highest for derivatives desks, structured products, and risk management teams.

Very high complexity. Requires: (1) Derivation and implementation of division-free Dupire residual in log-IV coordinates, (2) Quotient Fokker-Planck equation with mixed derivative terms, (3) DeepONet branch-trunk architecture with C2 activations and multiple coupled heads, (4) FNO spectral convolution alternative, (5) Complex multi-term residual objective with normalization and curriculum, (6) Annealed heterogeneous teacher supervision, (7) Residual-gated inference with OOD detection, (8) Integration with existing 2D PDE pricing engines (ADI, FD, MC), (9) Particle reference implementation for validation. The mathematical prerequisites include stochastic calculus, PDE theory, and functional analysis.

The paper provides detailed mathematical derivations, architecture descriptions, and training procedures. However, no code or repository is mentioned. Experiments use synthetic rough-Bergomi market states with specific parameters (48 training/12 test surfaces, 6 maturities x 11 log-moneyness nodes). The Heston-type backbone and particle reference are described but not publicly released. Reproduction would require implementing the full residual system, curriculum training, and particle reference from scratch.