Meta-Learning Neural Process for Implied Volatility Surfaces with SABR-induced Priors (2509.11928v1)

Abstract: Constructing the implied volatility surface (IVS) is reframed as a meta-learning problem training across trading days to learn a general process that reconstructs a full IVS from few quotes, eliminating daily recalibration. We introduce the Volatility Neural Process, an attention-based model that uses a two-stage training: pre-training on SABR-generated surfaces to encode a financial prior, followed by fine-tuning on market data. On S&P 500 options (2006-2023; out-of-sample 2019-2023), our model outperforms SABR, SSVI, Gaussian Process, and an ablation trained only on real data. Relative to the ablation, the SABR-induced prior reduces RMSE by about 40% and dominates in mid- and long-maturity regions where quotes are sparse. The learned prior suppresses large errors, providing a practical, data-efficient route to stable IVS construction with a single deployable model.