Arbitrage-Free Option Price Surfaces via Chebyshev Tensor Bases and a Hamiltonian Fog Post-Fit

Battle Count: 67

Highly relevant to quantitative trading in options markets. The method directly addresses the core production problem of constructing smooth, arbitrage-free option price surfaces from noisy market data. Applications include market making (tight bid-ask management), risk management (reliable Greeks from consistent surfaces), portfolio hedging, and regulatory marking. The fog post-fit mechanism for handling stressed/noisy regimes is particularly relevant for trading during volatile periods. However, the paper is primarily theoretical with no empirical validation tables, limiting immediate practical applicability.

High implementation complexity. Requires: (1) Chebyshev polynomial evaluation via Clenshaw recurrences, (2) coordinate warping (asinh, sqrt), (3) construction of design matrices and derivative blocks via chain rule, (4) collocation grid setup with no-arbitrage operators, (5) assembly of a large sparse QP with multiple regularization terms, (6) GCV-based hyperparameter selection, (7) mu-controller for coverage targeting, (8) lambda_NA grid search, (9) badness map computation and patch decomposition, (10) 3D fog lattice construction with Hamiltonian energy, (11) joint convex optimization for patch post-fit. The mathematical sophistication is very high, though individual components use standard numerical tools (OSQP, QR factorization, DCT).

The paper provides extremely detailed mathematical formulations, explicit parameter choices (basis sizes K=28-40, L=22-32; OSQP tolerances 4.5e-7; GCV on 8% subsample; lambda_NA ladder; mu-controller), and complete algorithmic descriptions. However, no code repository is provided, no specific dataset is named, and empirical results tables are absent from the extract. The methodology is fully specified mathematically but practical reproduction requires implementing the Chebyshev basis, collocation grid operators, QP assembly, and fog post-fit from scratch.