Meta-Learning Neural Process for Implied Volatility Surfaces with SABR-induced Priors

Paper: arXiv 2509.11928

Authors: Jirong Zhuang, Xuan Wu

Abstract

We treat implied volatility surface (IVS) reconstruction as a learning problem guided by two principles. First, we adopt a meta-learning view that trains across trading days to learn a procedure that maps sparse option quotes to a full IVS via conditional prediction, avoiding per-day calibration at test time. Second, we impose a structural prior via transfer learning: pre-train on SABR-generated dataset to encode geometric prior, then fine-tune on historical market dataset to align with empirical patterns. We implement both principles in a single attention-based Neural Process (Volatility Neural Process, VolNP) that produces a complete IVS from a sparse context set in one forward pass. On SPX options, the VolNP outperforms SABR, SSVI, and Gaussian process. Relative to an ablation trained only on market data, the SABR-induced prior reduces RMSE by about 40% and suppresses large errors, with pronounced gains at long maturities where quotes are sparse. The resulting model is fast (single pass), stable (no daily recalibration), and practical for deployment at scale.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced mathematics including neural process theory, attention mechanisms, and meta-learning frameworks, scoring high on math complexity. It provides concrete empirical results with specific metrics (40% RMSE reduction), compares to baselines (SABR, SSVI, Gaussian process), and discusses practical deployment, indicating strong empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal: Learn IVS from sparse options data<br/>Avoid per-day calibration, incorporate structural prior"] --> B["Methodology: Volatility Neural Process VolNP<br/>Attention-based meta-learning + SABR transfer learning"]
  B --> C["Data & Inputs: SPX Options Data"]
  B --> D["SABR-generated synthetic dataset<br/>(Geometric Prior Encoding)"]
  C --> E["Computational Process: Meta-training across trading days<br/>Conditional prediction for full IVS"]
  D --> E
  E --> F["Key Findings/Outcomes"]
  F --> G["Accuracy: 40% RMSE reduction vs. market-only ablation"]
  F --> H["Robustness: Stable, fast (single pass)<br/>No daily recalibration needed"]
  F --> I["Generalization: Strong gains at long maturities<br/>Outperforms SABR, SSVI, Gaussian Process"]
```mermaid
flowchart TD
  A["Research Goal: Learn IVS from sparse options data<br/>Avoid per-day calibration, incorporate structural prior"] --> B["Methodology: Volatility Neural Process VolNP<br/>Attention-based meta-learning + SABR transfer learning"]
  B --> C["Data & Inputs: SPX Options Data"]
  B --> D["SABR-generated synthetic dataset<br/>(Geometric Prior Encoding)"]
  C --> E["Computational Process: Meta-training across trading days<br/>Conditional prediction for full IVS"]
  D --> E
  E --> F["Key Findings/Outcomes"]
  F --> G["Accuracy: 40% RMSE reduction vs. market-only ablation"]
  F --> H["Robustness: Stable, fast (single pass)<br/>No daily recalibration needed"]
  F --> I["Generalization: Strong gains at long maturities<br/>Outperforms SABR, SSVI, Gaussian Process"]

Cited References (25)

1. Managing Smile Risk (2002)
2. A parsimonious arbitrage-free implied volatility parameterization with application to the valuation of volatility derivatives (2004)
3. Arbitrage-free SVI volatility surfaces (2014)
4. Beyond surrogate modeling: Learning the local volatility via shape constraints (2021)
5. Deep smoothing of the implied volatility surface (2020)
6. Incorporating prior financial domain knowledge into neural networks for implied volatility surface prediction (2021)
7. Operator Deep Smoothing for Implied Volatility — → 2406.11520
8. No-Arbitrage Deep Calibration for Volatility Smile and Skewness — → 2310.16703

2 of 25 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.