Meta-Learning Neural Process for Implied Volatility Surfaces with SABR-induced Priors
Meta-Learning Neural Process for Implied Volatility Surfaces with SABR-induced Priors
This paper proposes a meta-learning framework for reconstructing implied volatility surfaces (IVS) from sparse option quotes, implemented via the Volatility Neural Process (VolNP). VolNP is an attention-based neural process that learns a mapping from a small context set of quotes to a full IVS in a single forward pass, eliminating the need for per-day recalibration. To improve robustness, the model is pre-trained on synthetic IVS generated by the SABR model to encode a geometric prior, then fine-tuned on historical market data to adapt to empirical patterns.
Experiments on SPX options from 2006 to 2023 show that VolNP with SABR-induced prior (VolNP-SP) achieves the lowest RMSE (96.04 BPS) and MAE (48.22 BPS), outperforming SABR, SSVI, and Gaussian process baselines. The SABR prior reduces RMSE by approximately 40% compared to an ablation trained only on market data, with pronounced gains in long-maturity regions where quotes are sparse. VolNP-SP also produces arbitrage-free surfaces under market stress, as demonstrated during the COVID-19 volatility shock, and is computationally efficient (~25 ms per evaluation), making it practical for real-time deployment. The work highlights the effectiveness of combining meta-learning with transfer learning from structural models for robust IVS construction.
Highlights
- 1Frames IVS reconstruction as a meta-learning problem, eliminating per-day recalibration.
- 2Introduces VolNP, an attention-based neural process that maps sparse quotes to a full IVS in one forward pass.
- 3Uses transfer learning with SABR-induced priors to encode geometric plausibility, reducing RMSE by ~40%.
- 4Outperforms SABR, SSVI, and Gaussian process on SPX options, especially in sparse long-maturity regions.
- 5Produces arbitrage-free surfaces under market stress, unlike the ablation without SABR prior.
Methods
- MMeta-learning via Neural Process (VolNP) with self-attention encoder and cross-attention decoder.
- MTwo-stage training: pre-training on SABR-generated synthetic surfaces, then fine-tuning on historical market data.
- MNegative log-likelihood (NLL) loss for conditional predictive distribution.
- MEvaluation against SABR, SSVI, Gaussian process, and ablation (VolNP-Base) on SPX options from 2006-2023.
Results
- RVolNP-SP achieves overall RMSE of 96.04 BPS and MAE of 48.22 BPS, outperforming all benchmarks.
- RSABR-induced prior reduces RMSE by ~40% compared to VolNP-Base (trained only on market data).
- RVolNP-SP maintains low error and near-neutral bias in long-maturity regions where benchmarks fail.
- RVolNP-SP is computationally efficient (~25 ms per evaluation), enabling intraday updates.
- RVolNP-SP produces arbitrage-free surfaces (no butterfly arbitrage) under market stress, unlike VolNP-Base.
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