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

TL;DR

A SABR-informed multitask Gaussian process for constructing implied volatility surfaces from sparse option quotes that achieves lower error than the single-task Gaussian process and SABR and remains competitive at long-term maturities, while satisfying standard no-arbitrage conditions.

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.

Figures (11)

• Figure 1: Distribution of generated Heston "market" data points (target task $\mathcal{D}_\mathcal{T}$) in our experiments, by strike price and time to maturity. Dashed red lines indicate evaluation maturities.
• Figure 2: Evolution of calibrated SABR parameters ($\alpha, \beta, \rho, \nu$) across maturity slices for the Base Heston scenario. Note $\beta$ was fixed at 0.5 during calibration.
• Figure 3: Implied volatility curve comparison and residuals under the Base Heston scenario for near-term
• Figure 4: Implied volatility curve comparison and residuals under the Base Heston scenario for long-term
• Figure 5: No-arbitrage test. Panel (a) visualizes butterfly spreads; most methods remain above the zero line within a small tolerance band, while NN and GP occasionally dip negative at mid/long maturities. Panel (b) shows six panels of total variance $w(k,\tau)$ curves for SABR, SSVI, Cubic Spline, GP, SABR-MTGP, and NN; for most methods the level of $w$ increases with maturity at fixed $k$ and the $k$-profiles are smooth, with minor departures mainly for NN and GP.