SABR-Informed Multitask Gaussian Process: A Synthetic-to-Real Framework for Implied Volatility Surface Construction

This study introduces a SABR-informed multitask Gaussian process for constructing implied volatility surfaces from sparse option quotes. We treat a dense synthetic dataset generated by a calibrated SABR model as the source task and market option quotes as the target task. Within the multitask Gaussian process framework, we learn cross-task dependence via task embeddings with hierarchical regularization, enabling adaptive transfer of structural information. On Heston ground truth across ten market regimes and in a case study with SPX options, the model achieves lower error than the single-task Gaussian process and SABR at near-term maturities and remains competitive at long-term maturities, while satisfying standard no-arbitrage conditions. The framework combines the theory-driven structure with nonparametric Bayesian regression and yields reliable implied volatility surfaces for risk management.