Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces

Battle Count: 86

The paper is primarily relevant to derivatives pricing, risk management, and implied volatility surface modeling rather than direct trading strategies. It provides a framework for ensuring generated volatility surfaces are arbitrage-free, which is critical for consistent option pricing and hedging. The latent-space correction approach could be used in production systems that generate scenario surfaces for portfolio risk assessment. However, it does not directly address trading signals, execution, or portfolio construction.

The theoretical framework requires understanding of Hamilton-Jacobi PDEs, viscosity solutions, level-set methods, and no-arbitrage conditions in total variance space. Numerical implementation involves upwind/Godunov schemes, reinitialization, adaptive refinement, and sign-changing edge detection. Training and evaluating VAEs on Heston surfaces adds ML engineering complexity. The architecture-agnostic nature means the margin computation (decoding full surfaces + checking constraints on grids) is the dominant cost per evaluation.

The paper provides detailed numerical schemes (upwind discretization, Godunov Hamiltonian, reinitialization), grid specifications, VAE architecture details (encoder widths, activations, KL weight), and explicit analytic formulas for toy examples. However, no code repository is mentioned, and the Heston surface generation parameters (30,000 surfaces, specific grid) are described but not provided as downloadable data. Five training seeds are reported with statistics.