GARCH & Volatility Forecasting

Python-based volatility forecasting framework using GARCH(1,1), EGARCH, GJR-GARCH, and HAR-RV models with rolling estimation, regime classification, and predictive accuracy evaluation across multi-asset portfolios.

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Overview

Volatility forecasting is central to market risk management — from VaR estimation to options pricing and portfolio construction. This project builds a comprehensive suite of volatility models, evaluates short-horizon predictive accuracy, and tests robustness across market regimes including crisis and low-volatility periods.

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Models Implemented

GARCH(1,1)

• Maximum likelihood estimation
• Conditional variance dynamics
• Persistence and mean reversion analysis
• 22-day ahead volatility forecasting

EGARCH

• Asymmetric volatility response (leverage effect)
• Log-variance specification
• News impact curve analysis
• Comparison with symmetric GARCH

GJR-GARCH

• Threshold effects for negative returns
• Asymmetry coefficient estimation
• AIC/BIC model comparison

HAR-RV (Heterogeneous Autoregressive Realized Variance)

• Daily, weekly, monthly realized variance components
• Long-memory volatility properties
• Corsi (2009) methodology

EWMA (RiskMetrics)

• Lambda decay factor (0.94 standard)
• Benchmark comparison model

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Rolling Estimation and Regime Analysis

• Rolling windows: 21-day, 63-day, 126-day, 252-day
• Volatility regime classification: Low, Medium, High
• EWMA vs rolling volatility comparison
• Structural break and clustering analysis

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Forecast Evaluation

• MSE and QLIKE loss functions
• Diebold-Mariano test for forecast comparison
• Walk-forward out-of-sample validation
• Realized variance as benchmark proxy

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Tech Stack

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Project Structure

GARCH-Volatility-Forecasting/
│
├── data/
│   ├── returns.csv
│   └── prices.csv
│
├── notebooks/
│   ├── 01_garch_estimation.ipynb
│   ├── 02_egarch_gjr_garch.ipynb
│   ├── 03_har_rv_model.ipynb
│   ├── 04_rolling_estimation.ipynb
│   └── 05_forecast_evaluation.ipynb
│
├── src/
│   ├── garch_models.py
│   ├── har_rv.py
│   ├── rolling_vol.py
│   └── forecast_evaluation.py
│
├── results/
│   ├── garch11_conditional_vol.png
│   ├── egarch_gjr_comparison.png
│   ├── news_impact_curves.png
│   ├── har_rv_fit.png
│   ├── rolling_volatility_windows.png
│   ├── volatility_regimes.png
│   ├── forecast_evaluation.png
│   ├── har_rv_parameters.csv
│   ├── volatility_regimes.csv
│   └── forecast_evaluation.csv
│
└── README.md

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Key Results

• EGARCH outperforms GARCH(1,1) during high-volatility regimes by capturing the leverage effect in equity returns
• HAR-RV provides superior long-horizon forecasts (5-day, 22-day) compared to GARCH-family models
• Rolling 63-day GARCH estimates show faster regime adaptation than 252-day windows during market stress
• QLIKE loss confirms EGARCH as the preferred model for short-horizon risk forecasting applications

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Applications

• Short-horizon VaR and Expected Shortfall estimation
• Options pricing and volatility surface calibration
• Portfolio risk monitoring and drawdown alerts
• Regulatory capital modeling under FRTB

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References

• Engle, R. (1982) — Autoregressive Conditional Heteroskedasticity
• Nelson, D. (1991) — Conditional Heteroskedasticity in Asset Returns
• Corsi, F. (2009) — A Simple Approximate Long-Memory Model (HAR-RV)
• Andersen and Bollerslev (1998) — Answering the Skeptics