Detecting Put Skew Anomalies with Graph Embeddings

Put skew—elevated volatility at out-of-the-money put strikes—often contains signals about investor fears and market crashes. Anomalous put skew (deviations from historical norms) can indicate unusual hedging demand or information asymmetries. Graph neural networks, which learn representations of complex relationships, excel at detecting skew anomalies by capturing non-local structure in volatility surfaces.

Put Skew Patterns

In normal times, put skew follows a stable pattern: volatility increases as strikes fall below ATM, reflecting jump-down and crash risk. The slope and curvature of the put skew varies over time.

Anomalies: sudden steepening, unusual curvature, or rapid reversal of skew often precede market dislocations. Classic example: large OTM put buying before known risks (earnings, Fed announcement).

Why Graph Embeddings?

A volatility surface is a graph: nodes are (strike, maturity) points, edges connect neighboring points. Put skew exhibits non-local structure: skew at one strike influences skew at others through arbitrage constraints and market microstructure.

Graph neural networks (GNNs) propagate information across the surface, learning global patterns rather than local features. Nodes aggregate information from neighbors iteratively, enabling detection of anomalies that span multiple strikes/maturities.

Graph Construction

Build the graph from the volatility surface:

• Nodes: each (strike, maturity) point with features (implied vol, bid-ask spread, recent volume)
• Edges: connect each node to neighboring strikes and maturities
• Node features: implied vol level, skew relative to neighbors, recent changes

GNN Architecture for Anomaly Detection

Use a graph autoencoder approach:

• Encoder: GNN learns compressed representation of the volatility surface
• Decoder: reconstructs the surface from the compressed representation
• Training: minimize reconstruction error on normal volatility surfaces
• Inference: compare actual surface to reconstruction; large errors indicate anomalies

Normal surfaces compress well and reconstruct accurately. Anomalous surfaces do not—the encoder struggles to represent unusual structures efficiently.

Alternative: Semi-Supervised Learning

If some anomalous surfaces are labeled (from history of known events), use semi-supervised learning:

• Labeled data: known-anomaly surfaces
• Unlabeled data: normal historical surfaces
• GNN classifier learns to identify anomalies using both labeled and unlabeled data

Temporal Dynamics and Recurrent GNNs

Volatility surfaces evolve over time. A recurrent GNN (combining GNN with LSTM-like temporal modeling) can capture both spatial structure (across strikes) and temporal dynamics (evolution over time).

Anomalies manifest not just as unusual current surface shapes, but as unusual transitions between surfaces over time.

Practical Anomaly Responses

When anomalous put skew is detected:

• Hedging: increase hedge ratios (buy more tail hedges)
• Trading: sell expensive OTM puts if skew appears excessive
• Risk management: tighten position limits to reduce tail risk exposure
• Research: investigate cause of anomaly (what news or event precipitated it?)

Challenges and Limitations

GNN anomaly detection requires sufficient historical data to establish baseline normality. In new markets or after market structure changes, historical patterns may not apply.

Also, some "anomalies" have rational explanations (earnings, known upcoming events). The detector should flag deviations from historical patterns, but interpretation requires domain expertise.

Conclusion

Graph neural networks leverage the network structure of volatility surfaces to detect anomalous put skew patterns that precede market stress. This sophisticated application of GNNs demonstrates how graph-based learning captures complex relational structure in derivatives data.