DeepVol: Neural Volatility Surface Modeling & Forecasting

DeepVol is a comprehensive quantitative finance library designed for high-fidelity volatility surface modeling, risk-neutral density (RND) extraction, and predictive analytics using deep learning. This project bridges classical stochastic modeling with modern machine learning architectures, specifically leveraging a Mixture-of-Experts (MoE) network to forecast implied volatility dynamics.

🌟 Key Features

• Arbitrage-Free Surface Calibration: Implementation of SVI (Slice) and global SSVI (Surface) models with strict adherence to no-arbitrage constraints.
• Risk-Neutral Density (RND) Extraction: Derivation of probability density functions (PDF) via the Breeden-Litzenberger identity, providing higher-order moments (Skewness, Kurtosis) for tail-risk analysis.
• Neural Volatility Forecasting: A regime-aware Mixture-of-Experts (MoE) architecture that specializes in predicting 10-day changes in total variance.
• Automated Data Pipeline: End-to-end orchestration from live market data ingestion (Yahoo Finance) to feature engineering and Parquet-based persistence.
• Vectorized Engineering: High-throughput Black-Scholes pricing and IV inversion using optimized NumPy operations and Brent’s method.

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🏗 Quantitative Engine

1. Volatility Surface Modeling (src/models/)

The framework supports two primary calibration routines to ensure a smooth, arbitrage-free surface:

• SVI (Stochastic Volatility Inspired): Calibrates individual expiry slices using the Gatheral (2004) parameterization:

$$w(k) = a + b(\rho(k-m) + \sqrt{(k-m)^2 + \sigma^2})$$

• Global SSVI (Surface SVI): Fits the entire surface simultaneously to ensure term-structure consistency and eliminate calendar arbitrage:

$$w(k, \theta) = \frac{\theta}{2} \left[ 1 + \rho \phi(\theta) k + \sqrt{(\phi(\theta) k + \rho)^2 + (1 - \rho^2)} \right]$$

with the power-law function $$\phi(\theta) = \eta \theta^{-\gamma}$$

2. Risk-Neutral Density Extraction (src/features.py)

Utilizing the Breeden-Litzenberger identity, the library reconstructs the market-implied PDF from the calibrated surface:

$$f(K) = e^{rT} \frac{\partial^2 C}{\partial K^2}$$

The module performs numerical integration via Simpson’s rule on a 5,000-point grid to extract:

• Skewness & Kurtosis: Quantifying market-implied asymmetry and tail risk.
• Martingale Diagnostic: Monitoring the error to ensure model consistency with the forward price. $$|E^{RN}[S_T] - F|$$

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🧠 Mixture-of-Experts (MoE) Forecasting

The forecasting engine utilizes a specialized deep learning architecture to predict the 10-trading-day change in total variance (h=10):

$$y_t = w_{t+h} - w_t$$

Architecture & Design

• LSTM Encoder: Processes historical sequences of volatility and regime features.
• Regime-Aware Gating: A gating network maps input features (e.g., IV z-scores, momentum, term-structure slope) to mixture weights over 4 specialized expert heads.
• Feature Enrichment: Includes rolling z-scores, IV momentum, and volatility-of-volatility (vol-of-vol) indicators to capture shifting market regimes.
• Physics-Informed Sample Weighting: Employs a "physics-based weight-decay" mechanism that penalizes the loss function for training samples exhibiting high SVI/SSVI fit costs, calendar arbitrage violations, or RND martingale errors.
• Benchmark Performance: The MoE model achieves a 7.7% MAE improvement over the σ -persistence baseline.

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📂 Project Structure

.
├── src/
│   ├── models/
│   │   ├── bs_engine.py        # Vectorized BS pricing & Brent IV inversion
│   │   └── svi_fit.py          # SVI and SSVI surface fitting logic
│   ├── features.py             # RND moment extraction (skew, kurtosis)
│   └── data_loader.py          # Live data ingestion & cleaning
├── main.py                     # Live production pipeline orchestrator
├── historical_pipeline.py      # Historical backtesting & dataset generation
├── moe_feature_enrichment.py   # ML feature engineering (regime indicators)
├── notebooks/                  # Research & development walkthroughs
├── moe_forecaster.ipynb        #model notebook
├── moe_forecaster.pt           #model
├── batch_process_tickers.py    # script for multiple-ticker processing in historical pipeline
├──setup.py
├── requirements.txt
└── README.md

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🚀 Getting Started

Installation

git clone https://github.com/alexmilekhin/deepvol.git
cd deepvol
pip install -e .

Running the Live Pipeline

Calibrate the surface and extract features for a specific ticker.

python main.py --ticker {TICKER} --data-dir ./data --metrics-dir ./results

The pipeline automatically fetches the current 13-week Treasury yield (^IRX) as the risk-free rate proxy.

Training Data Generation

Process historical data to generate enriched feature sets for ML training:

python historical_pipeline.py --file data/options_data.parquet --ticker {TICKER}
python moe_feature_enrichment.py --input historical_results/historical_svi_{TICKER}.parquet

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📝 License & Author

Author: Alexander Milekhin — milekhin.alexander@gmail.com

Distributed under the MIT License. See LICENSE for more information.