Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces
Read the original on arXiv AI →The paper investigates how generative models for implied volatility surfaces must respect static no‑arbitrage constraints. By mapping latent codes to surfaces, it defines a scalar margin for each code and identifies the admissible latent set where this margin is nonnegative. The authors prove that admissible codes remain admissible under small perturbations, characterize the boundary via a zero‑margin condition, and derive a level‑set equation guiding dynamics toward this boundary. The framework applies broadly to models such as variational autoencoders and GANs, and numerical experiments confirm known boundaries in analytic examples and demonstrate how the boundary can correct violating latent codes.
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