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Graph-Based Modeling of Financial Volatility Dynamics

Chuanzhen Wang, Alice Zhang, Wei Chen, Michael Brown

arXiv:2608.26127v1q-fin.STcs.CLcs.LG

TL;DR

Forecasting realized volatility from IV surfaces is difficult because static-image methods do not capture their temporal dynamics. FA-GSTN models IV-surface evolution with a finance-aware spatio-temporal graph, achieving state-of-the-art accuracy, data efficiency, and stress-period robustness.

  • Problem

    Static-image approaches to IV surfaces fail to capture the surface’s inherent temporal dynamics, despite IV containing rich predictive information for realized volatility.

  • Method

    FA-GSTN constructs spatio-temporal graph sequences with adaptive spatial and explicit temporal edges, finance-aware node features, smoothing, and adaptive robust loss.

  • Results

    FA-GSTN establishes a new state of the art, including R2 = 0.372 versus 0.315 for the best Vision Transformer baseline with one year of training.

  • Takeaways & Limitations

    Explicit temporal modeling and financial inductive biases support accurate, data-efficient, and robust realized-volatility forecasting from IV surfaces.

Abstract

from arXiv · show

Accurate forecasting of realized volatility ($RV$) is crucial for risk management and derivatives pricing. Although the implied volatility ($IV$) surface offers rich informational content, prevailing methods that treat it as a static image fail to capture its inherent dynamics. To overcome this limitation, we propose the Finance-Aware Graph Spatio-Temporal Network (FA-GSTN), a novel architecture that reframes $RV$ forecasting as modeling the evolution of a structured financial object. FA-GSTN builds a spatio-temporal graph sequence from the $IV$ surface, where nodes correspond to grid points and edges encode adaptive spatial (intra-day) and explicit temporal (inter-day) dependencies. The model incorporates domain knowledge through finance-aware node features (e.g., option Greeks) and tackles high-frequency noise via a multi-scale temporal smoothing gate coupled with an adaptive robust loss function. Comprehensive evaluations on a large-scale equity options dataset show that FA-GSTN sets a new state of the art, delivering superior predictive accuracy ($R^2$ up to 0.473). It also demonstrates remarkable data efficiency, substantially outperforming strong Vision Transformer baselines when trained on only one year of data ($R^2$: 0.372 vs. 0.315). Furthermore, the model exhibits enhanced robustness during periods of market stress, such as 2020--2021. Ablation studies confirm the vital roles of the spatio-temporal graph structure, finance-aware components, and integrated noise-handling modules. Our work underscores the substantial benefits of explicitly modeling temporal dynamics and infusing financial inductive biases for accurate and robust volatility forecasting.

1 Introduction

Realized volatility forecasting matters for quantitative finance, but static-image methods fail to represent the IV surface’s financial structure and temporal evolution. FA-GSTN addresses this gap with finance-aware spatio-temporal graph modeling and achieves strong accuracy, data efficiency, and robustness.

  • Realized volatility forecasting supports derivatives pricing, portfolio optimization, risk management, and regulatory capital allocation.
  • Static-image approaches overlook the IV surface’s financial structure and temporal dynamics.
  • FA-GSTN represents IV surfaces as structured spatio-temporal graphs with adaptive spatial connections and explicit temporal links.
  • Finance-aware node features incorporate option Greeks, while smoothing and robust-loss modules address high-frequency noise and outliers.
  • 0.372 versus 0.315: FA-GSTN outperforms the best Vision Transformer baseline when trained on one year of data.This corresponds to an 18% relative improvement.
  • Ablations confirm significant and complementary gains from the graph structure, finance-aware features, and noise-handling modules.

2 Related Work

Prior deep-learning approaches commonly use IV surfaces as static images, capturing spatial patterns without modeling their temporal evolution. Vision Transformers extend this image-based paradigm but may still process time steps independently.

  • Prior IV-surface prediction methods use hand-crafted features or convolutional networks operating on single-day surfaces.
  • These approaches capture spatial patterns but do not model temporal evolution across the surface.
  • Vision Transformers treat IV surfaces as single-channel images and may not fully capture dynamic interdependencies across time.

3 Methodology: Finance-Aware Graph Spatio-Temporal Forecasting

FA-GSTN treats the evolving IV surface as a structured multivariate object rather than independent image snapshots. Its graph sequence separates adaptive intra-day financial relationships from explicit inter-day continuity for RV forecasting.

  • The methodology targets temporal dynamics, high-frequency noise, and data-efficient learning in realized-volatility forecasting.
  • Each day’s smoothed IV grid is used to forecast future realized volatility over a horizon H, such as 28 calendar days.
  • FA-GSTN constructs a lookback sequence of graphs with distinct intra-day spatial and inter-day temporal edge families.
  • Adaptive spatial adjacency learns connections from financial distance between IV-grid nodes rather than relying only on fixed image neighborhoods.
  • Temporal edges connect each node to its counterpart on the preceding day, forming chains that capture IV-surface evolution.

3.2 Finance-Aware Node Feature Initialization

FA-GSTN initializes graph nodes with domain-informed signals to improve data efficiency. The feature vector includes IV information, temporal context, and Black–Scholes option sensitivities.

  • Initial node features incorporate domain knowledge to enhance data efficiency.
  • The feature vector concatenates multiple informative signals at each delta–maturity grid location.
  • Delta, Vega, and Charm are Black–Scholes sensitivity parameters computed using the forward price and risk-free rate.
  • These Greeks provide theory-grounded inductive biases about option price sensitivity.

3.3 FA-GSTN Architecture

FA-GSTN processes an IV-surface graph sequence with multi-scale temporal smoothing, spatio-temporal graph convolution, and attention-based readout to forecast RV.

  • Multi-Scale Temporal Smoothing and Gating: Parallel temporal smoothing applies multiple operators to each node’s raw IV feature sequence before adaptive gating.The smoothing operators include the raw series and alternatives such as moving averages and exponentially weighted moving averages.
  • Multi-Scale Temporal Smoothing and Gating: A learnable gating mechanism assigns adaptive weights to the original and smoothed feature series for active noise suppression.The resulting noise-filtered IV feature combines information across these temporal representations.
  • Spatio-Temporal Graph Convolution Block: STGC blocks aggregate node information across spatial and temporal edges to update graph representations.Spatial aggregation uses finance-aware neighbors, temporal propagation carries information across time, and the update includes a residual connection.
  • Prediction Readout: After M STGC blocks, an attention-based readout weights the latest graph’s nodes by relevance to RV prediction.The graph-level summary is passed through a fully connected prediction network to produce the final forecast.

3.4 Adaptive Robust Optimization

FA-GSTN uses an Adaptive Robust Loss to address non-stationary noise and outliers in financial targets during end-to-end training.

  • Adaptive Robust Loss: The Adaptive Robust Loss generalizes the Huber loss by combining quantile-like weighting with a dynamic boundary parameter dt.This design adapts the objective to changing target noise and outlier behavior.
  • Adaptive Robust Loss: wt down-weights the highest residuals, while dt is learned per batch from an initialization based on residual dispersion.The resulting loss adapts to local noise levels and provides more robust gradients than a fixed Huber loss.

3.5 Summary of Advantages over Baseline ViT

FA-GSTN improves on the static-image ViT baseline by explicitly modeling temporal dynamics, integrating noise handling, and embedding financial domain knowledge.

  • Explicit Temporal Dynamics: Spatio-temporal graph modeling and STGC blocks explicitly represent IV-surface evolution, including trends, mean reversion, and volatility clustering.This addresses the temporal-dynamics limitation of static-image processing.
  • Integrated Noise Handling: Multi-scale smoothing gating and adaptive robust loss address high-frequency noise and outliers at both feature and objective levels.The two mechanisms provide integrated noise handling within the forecasting pipeline.
  • Strong Domain Inductive Bias: Finance-aware node features based on Greeks and adaptive spatial adjacency embed structured financial knowledge for sample-efficient, interpretable representations.These components provide a strong domain inductive bias beyond the static-image ViT baseline.

4 Experimental Results

The experiments evaluate FA-GSTN against MLP and ViT baselines across predictive performance, data efficiency, and market conditions. FA-GSTN consistently leads, including in one-year training and stressed-market settings.

  • Experimental Setup: The evaluation compares FA-GSTN with MLP and ViT baselines across overall accuracy, data efficiency, and robustness to market conditions.The experiments use realized volatility forecasting from implied volatility surfaces and replicate the high-level protocol used for ViT baselines.
  • Main Results: FA-GSTN consistently achieves the highest R2 across all training regimes.The comparison covers models trained on 1, 4, and 10 years of historical data and tested on the subsequent year.
  • Data Efficiency: 0.372 R2 with one year of training data exceeds the best baseline’s 0.315 under the same condition.With ten years of data, FA-GSTN reaches its best overall performance of R2 = 0.473.
  • Data Efficiency: FA-GSTN achieves the highest average R2 and the most stable yearly performance in the one-year training setting.Its lower standard deviation indicates greater stability across test years, while ViT models show more volatile yearly performance.
  • Robustness: FA-GSTN significantly outperforms all baselines during the challenging 2020–2021 test years.The model’s explicit spatio-temporal modeling captures evolving dynamics and contagion effects during market stress.
  • Summary: The results attribute FA-GSTN’s gains to structured spatio-temporal graph forecasting, finance-aware features, and integrated noise handling.These components support performance across data volumes and more stable behavior during market stress.

5 Ablation Studies

Ablation studies show that FA-GSTN’s full integration of temporal structure, finance-aware components, and noise handling produces the strongest performance. Explicit temporal modeling is most consequential, while finance-aware features are especially valuable with limited data.

  • Core Architectural Components: The full integration of FA-GSTN modules yields the best performance in the core ablation study.Models are trained on 2018–2021 data and evaluated on the 2022 test set using out-of-sample R2.
  • Core Architectural Components: R2 = 0.352 for the Static-Graph Baseline represents the most severe degradation after removing explicit temporal dynamics.The reported drop is 0.130, identifying the spatio-temporal graph structure as the critical architectural component.
  • Core Architectural Components: Removing Adaptive Spatial Adjacency causes a ΔR2 = −0.081 decline, while removing Finance-Aware Node Features causes ΔR2 = −0.070.These results support learning financially relevant spatial relationships and incorporating option Greeks as useful inductive biases.
  • Impact Across Data Regimes: 0.060 is the Finance-Aware Features ablation drop with one year of training, compared with 0.045 and 0.031 for four and ten years.The module’s relative importance is greatest in the low-data regime.
  • Impact Across Data Regimes: The Temporal Smoothing Gate and Adaptive Robust Loss provide consistent gains across all evaluated data volumes.Their reported role is mitigating high-frequency noise and outliers across one-, four-, and ten-year training regimes.
  • Temporal Smoothing Gate: Learnable gating improves performance by 0.024 over simple concatenation of smoothed series.The gate dynamically selects the most informative smoothing scale for each node and time step.
  • Loss Function: The Adaptive Robust Loss outperforms standard alternatives by adjusting its transition point and down-weighting extreme residuals.Its dual mechanism adapts to local noise characteristics and improves robust generalization.
  • Summary: Ablations identify explicit temporal modeling as fundamental, finance-aware components as especially important for data efficiency, and noise-handling modules as consistent contributors.The findings emphasize complementary gains from the complete FA-GSTN design.

6 Further Evaluation

Further evaluations examine training dynamics, loss behavior, crisis-period forecasts, and learned spatial relationships. FA-GSTN shows steadier optimization, closer crisis tracking, and financially intuitive adjacency patterns than representative ViT baselines.

  • Training Dynamics: FA-GSTN’s validation R2 rises gradually and steadily before stabilizing, unlike ViT models that peak within 1–2 epochs and then plateau or decline.The pattern indicates more stable optimization and better generalization under identical training settings.
  • Training Dynamics: Adaptive Robust Loss produces a smoother descent and lower final loss than standard Huber or MSE loss.The comparison underscores its handling of financial-data outliers.
  • Crisis-Period Case Study: During the March 2020 COVID-19 volatility surge, FA-GSTN tracks actual realized volatility more closely with smaller deviations and fewer extreme errors.The ViT_1.7M baseline shows larger lag and overshooting in the SPY case study.
  • Spatial Interpretability: The learned adjacency matrix forms strong connections between nodes with similar maturities and similar moneyness.These patterns correspond to term-structure and smile/skew relationships in the IV surface.

7 Conclusion

FA-GSTN reframes evolving IV surfaces as dynamic spatio-temporal graphs and combines this structure with finance-aware features and noise-handling mechanisms. Experiments report state-of-the-art forecasting, data efficiency, robustness during market stress, and complementary gains from the core components.

  • Architecture: FA-GSTN reformulates IV surface sequences as dynamic spatio-temporal graphs with dedicated spatial and temporal edges.This departs from the static-image formulation used in prior work.
  • Architecture: FA-GSTN integrates option Greeks, adaptive multi-scale temporal smoothing, and Adaptive Robust Loss to improve data efficiency and robustness.These components provide finance-aware features and mechanisms for handling noisy temporal observations.
  • Empirical findings: 0.372 versus 0.315: FA-GSTN outperforms the best Vision Transformer baseline when trained on one year of data.The comparison is reported as a significant advantage under limited-data conditions.
  • Empirical findings: FA-GSTN achieves the highest out-of-sample R2 scores across training regimes using 1, 4, and 10 years of data.The evaluation identifies the model as establishing a new state of the art.
  • Empirical findings: The model exhibits enhanced robustness during the 2020–2021 market-stress episode.This robustness is reported alongside superior overall predictive performance.
  • Empirical findings: Ablations show significant and consistent gains from the graph structure, finance-aware features, adaptive adjacency, noise handling, and robust loss.The explicit spatio-temporal graph structure is identified as essential, while the other components provide complementary improvements.
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