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

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  • Jirong Zhuang
  • Xuan Wu

Abstract

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.

Suggested Citation

  • Jirong Zhuang & Xuan Wu, 2025. "SABR-Informed Multitask Gaussian Process: A Synthetic-to-Real Framework for Implied Volatility Surface Construction," Papers 2506.22888, arXiv.org, revised Feb 2026.
    • Handle: RePEc:arx:papers:2506.22888
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