Quantifying VIX Tail Risk

Research codebase comparing GARCH-family volatility models and Compound Poisson Process (CPP) jump models for VIX tail-risk quantification. The pipeline fits EGARCH/GARCH on daily VIX log changes, identifies shock events, models arrival rates and jump magnitudes, and evaluates VaR/CVaR with regime and out-of-sample checks.

Developed for IEDA4000E - Statistical Modelling for Financial Engineering at the Hong Kong University of Science and Technology (HKUST). Maintained under CttQuantLab.

Not financial advice. This repository is for research and education only. Historical results do not imply future performance.

Highlights

• GARCH(1,1) and EGARCH(1,1) with automatic GED/t/normal selection via PIT diagnostics
• Shock identification by quantile and volatility-relative thresholds
• Homogeneous and Hawkes arrival models plus Compound Poisson jump-risk estimation
• Regime analysis across pre-COVID, COVID, post-COVID, and recent windows
• Out-of-sample CPP forecast evaluation (2022-2025 holdout)
• Reproducible pipeline (runall.py), notebooks, tests, report, and slides

Headline results

Model / metric	Value	Notes
Best volatility fit	EGARCH(1,1), GED	AIC 27,395 vs GARCH 27,531
Volatility half-life	10.2 days	EGARCH persistence 0.934
CPP arrival rate	12.64 / year	Full-sample Poisson rate
CPP VaR (95%)	4.24	Annual cumulative shock impact
CPP CVaR (95%)	5.01	Expected shortfall
OOS forecast error	-17.8%	2022-2025; VaR not exceeded

Full tables and discussion: docs/SUMMARY.md, docs/report/report.pdf.

Repository layout

.
├── docs/
│   ├── SUMMARY.md           # Results digest
│   ├── report/              # Academic report (LaTeX + PDF)
│   └── slides/              # Beamer presentation (LaTeX + PDF)
├── figures/                 # Published plots by category
├── notebooks/               # Step-by-step analysis notebooks
├── src/                     # Core library modules
├── tests/                   # Pytest suite
├── runall.py                # End-to-end pipeline driver
├── requirements.txt
├── pyproject.toml
└── LICENSE

Quick start

git clone https://github.com/CttQuantLab/Quantifying-VIX-Tail-Risk.git
cd Quantifying-VIX-Tail-Risk

python -m venv .venv
source .venv/bin/activate  # Windows: .venv\Scripts\activate

pip install -U pip
pip install -r requirements.txt
pip install -e .

pytest -q

Run the pipeline

Download VIX data (Yahoo Finance), fit models, and regenerate figures:

python runall.py

Optional flags:

python runall.py --force-download   # refresh cached VIX history
python runall.py --skip-plots       # models only, no figure export

Outputs land under figures/ (grouped by topic) and cached data under data/raw/.

Data

• Source: Yahoo Finance ^VIX daily closes
• Window: 2010-01-05 to latest available (4,100+ business days in the published run)
• Preprocessing: business-day alignment, forward-fill, 0.1% winsorization, log-level and log-change features
• Train/test split: 75% train (2010-2021), 25% test (2022-2025) for forecast evaluation

Method sketch

Volatility. GARCH and EGARCH on daily log VIX changes; distribution chosen by PIT Kolmogorov-Smirnov fit.

Shocks. Threshold exceedances on standardized returns; inter-arrival times fit to Poisson and Hawkes processes.

Jump risk. Compound Poisson accumulation (S(T)=\sum_{i=1}^{N(T)} J_i) with Pareto jump sizes; Monte Carlo paths for VaR/CVaR.

See the report for full equations, parameter tables, and diagnostic figures.

Documentation

Document	Description
docs/SUMMARY.md	Condensed results and regime tables
docs/report/report.pdf	Full academic write-up
docs/slides/slides.pdf	Presentation deck
figures/	Standalone result figures

Development

pytest -q
pip install -e ".[dev]"

Random seeds default to 42 in src/config.py.

Citation

If this repository is useful for your work, please cite the course project report and link this repository:

@misc{chong2025vixtailrisk,
  author       = {Chandrean, Vittorio Prana and Chong, Tin Tak and Choi, Man Hou},
  title        = {Quantifying VIX Tail Risk: Volatility Clustering and Jump Processes},
  year         = {2025},
  howpublished = {\url{https://github.com/CttQuantLab/Quantifying-VIX-Tail-Risk}},
  note         = {IEDA4000E course project, HKUST}
}

See also CITATION.cff for machine-readable metadata.

References

1. Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics.
2. Nelson, D. B. (1991). Conditional Heteroskedasticity in Asset Returns. Econometrica.
3. Cont, R., and Tankov, P. (2004). Financial Modelling with Jump Processes. Chapman and Hall/CRC.
4. McNeil, A. J., Frey, R., and Embrechts, P. (2015). Quantitative Risk Management. Princeton University Press.

License

MIT License. See LICENSE.

Acknowledgments

• Course: IEDA4000E - Statistical Modelling for Financial Engineering, HKUST
• Authors: Vittorio Prana CHANDREAN, CHONG Tin Tak, CHOI Man Hou
• Core stack: arch, statsmodels, pandas, scipy, matplotlib, yfinance