Reaction-boundary variance and adjoint-consistent local-volatility projection

Battle Count: 79

The paper provides a structural decomposition of local volatility into interpretable microstructure quantities (liquidity slope, resilience, signed forcing, memory, activity), which is valuable for understanding volatility surface morphology and its sources. The adjoint-consistency framework for non-unique time projections is relevant for model risk and incompleteness in derivative pricing. However, the paper is primarily theoretical/analytical with stylized simulations rather than empirical calibration, limiting direct implementation for trading strategies. The connection to order-book dynamics and market impact is relevant for execution and market-making strategies.

The analytical framework involves Green-function calculations, spectral analysis with long-memory processes, Wiener-Khinchin filtering, asymptotic integral evaluations, and adjoint operator theory. Implementing the full pipeline requires: (1) solving the boundary response equation with Abel kernel, (2) computing finite-scale spectral cumulants, (3) evaluating the dimensionless response function F_gamma, (4) performing clock projection, (5) solving the resulting local-volatility PDE, and (6) verifying adjoint consistency for non-unique clocks. The numerical simulations are simpler but the full theoretical machinery is mathematically demanding.

The authors provide a versioned v1.0.0 reproducibility release on GitHub with simulation code and figure outputs. All analytical derivations are self-contained with explicit equations. However, the simulations use stylized/phenomenological parameters rather than empirical market data, limiting direct empirical reproducibility. The paper includes detailed appendices (A and B) with full derivations.