A Latent Flow Matching Method for Arbitrage-Aware Implied Volatility Surface Generation

This paper proposes an arbitrage-aware latent flow matching framework for unconditional generation of implied volatility surfaces. The framework first compresses high-dimensional surfaces into a low-dimensional latent space using a variational autoencoder with differentiable penalty regularization for calendar spreads, call spreads, and butterfly arbitrage. A flow matching model then learns to map a Gaussian prior to the empirical latent distribution, which is finally decoded back to a volatility surface. This method can generate 90.8% of surfaces that satisfy all tested static no-arbitrage conditions, performs best in the extreme Q99 range, and balances distributional similarity, tail preservation, and financial consistency without post-sampling reweighting.