Arbitrage-Free Volatility Modeling & Machine Learning Forecast Framework

Options Volatility Surface No-Arbitrage Modeling Transformer Time-Series Cross-Asset Features Scenario Analysis Explainable AI MLflow Python/PyTorch

Marsbridge developed a machine-learning framework for modeling and forecasting movements in implied volatility surfaces while ensuring no-arbitrage consistency. The system combined modern statistical learning with domain-aware constraints to generate explainable scenario forecasts and risk-aware recommendations. The hybrid approach—machine learning governed by rule-based validation—has since become a core Marsbridge pattern for producing robust, auditable ML models in derivatives analytics.

Customer

Client Global Options Portfolio Manager (Private)

Industry Systematic Volatility / Derivatives

Region US & Europe

The trading team needed an analytical engine to model volatility dynamics across multiple maturities and strikes, forecast short-term shifts in volatility shape, and generate interpretable indicators to inform strategy selection and risk control.

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

Modeling

Python, PyTorch, Transformer time-series models, Explainable AI libraries

Data & Validation

Pandas, statistical smoothing for arbitrage checks, Great Expectations for data QA

MLOps

MLflow for lineage tracking, containerized services for deployment

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.

Discovery & Data Review
Surface Modeling
Forecasting Model
Scenario Analytics
Deployment

Team

Quant Lead

ML Engineer

0.5

Data Engineer

0.5

MLOps

Marsbridge derivatives quant team modeling volatility

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.

Modernize Your Volatility Research

Looking to combine ML forecasting with risk controls? We design arbitrage-aware, explainable volatility frameworks that meet modern compliance and performance standards.

Start your project Schedule a consultation

Related Case Studies: Machine Learning & AI Solutions

Seasonality Detection & Predictive Modeling in Global Futures

Private Commodity Research Investor, USA

[Seasonality modeling] [Time-series ML] [Representation learning] [Pattern similarity] [Continuation vs. mean-reversion] [Backtesting at scale] [Explainability]

Seasonality Detection & Predictive Modeling in Global Futures