Arbitrage-Free Volatility Modeling & Machine Learning Forecast Framework

Customer

Challenge

Ensuring No-Arbitrage Consistency in ML Forecasts

• Arbitrage-free modeling: Forecasts must satisfy calendar and butterfly no-arbitrage conditions rather than rely on raw grid predictions.
• Sparse, noisy data: Quotation gaps and event-driven distortions required robust fitting and outlier handling.
• Bridging prediction and decision: The system needed to translate model outputs into practical trade analytics without exposing proprietary trade logic.
• Transparency: Model decisions had to remain interpretable and reproducible for regulatory and internal-risk review.

Solution

Three-Layer Volatility Modeling Architecture

Approach: A small Derivatives ML team—Quant Lead, ML Engineer, Data Engineer, and MLOps specialist—built a three-layer architecture consisting of a volatility-surface constructor, a forecasting model, and a scenario analytics layer.

Volatility Surface Construction

Implemented a no-arbitrage fitting process that adjusts the volatility lattice to maintain smoothness across moneyness and tenor. Introduced quality metrics and flags to identify illiquid or stale data points before modeling.

Machine-Learning Forecasting

Deployed a Transformer-based model to predict changes in key volatility parameters jointly across maturities and strikes. Employed regularization losses to discourage arbitrage violations and preserve local monotonicity. Added explainability tools (SHAP-style feature attributions) for model interpretation and audit.

Scenario Analytics & Recommendations

Built a scenario-testing layer that evaluates model forecasts under multiple market paths and reports expected risk/return envelopes rather than explicit trade instructions. Provided an interface for human review, allowing analysts to adjust confidence thresholds or override recommendations.

Technologies & tools

Process

Discovery & Data Review: Audit volatility data, identify coverage gaps, and define data-quality filters. Surface Modeling: Build a calibrated, arbitrage-free surface and benchmark against historical fits. Forecasting Model: Train the Transformer model on cleaned features; validate under cross-market regimes. Scenario Analytics: Evaluate risk envelopes and confidence bands through Monte-Carlo simulation. Deployment: Package as an internal API with explainability and monitoring dashboards.

1. Discovery & Data Review
2. Surface Modeling
3. Forecasting Model
4. Scenario Analytics
5. Deployment

Results

• Improved Stability: Improved forecast stability compared to baseline statistical models, reducing noise in daily volatility updates.
• Financially Coherent: Consistent arbitrage checks ensured outputs were financially coherent and regulator-friendly.
• Transparent Reporting: Transparent reporting allowed non-quant stakeholders to interpret the drivers of volatility changes.
• Scalable Architecture: Scalable architecture enabled re-use for new assets and regions without proprietary calibration details.

All metrics have been generalized for confidentiality. This case study represents methodology and outcomes only, not trading performance.