📈 Market Risk Modelling: VaR, ES & Copulas
📍 EPFL – Master in Financial Engineering, Year 2 (2025)
👥 Team: Matthias Wyss, William Jallot, Antoine Garin
📄 Final Report: Report
🔗 GitHub Repository: GitHub
This project evaluates market risk for a portfolio composed of technology and banking stocks (AAPL, META, JPM) over the 2023–2025 period. It covers the full risk management pipeline: from empirical stylized facts analysis to advanced tail-risk forecasting and dependence structure modeling.
🔍 Methodology & Components
- Empirical Analysis: Investigation of log-returns, volatility clustering, and fat tails. Jarque-Bera tests and QQ-plots confirm the non-normality of returns.
- Univariate Risk Forecasting: Implementation of several VaR and ES models:
- Historical Simulation (HS): Non-parametric baseline.
- Parametric Models: Gaussian and Student-t distributions.
- Conditional Models: AR(p)-GARCH(1,1) processes to capture time-varying volatility.
- Filtered Historical Simulation (FHS): Combining GARCH volatility with empirical innovation distributions.
- Dependence Modeling: Utilizing Copulas (Gaussian, Student-t, Clayton, Frank, Gumbel) to model the joint distribution of returns beyond linear correlation.
- Rigorous Backtesting: Evaluation of model accuracy using Kupiec (POF) tests for VaR and Acerbi-Székely tests for Expected Shortfall.
📊 Performance & Key Insights
The results provide evidence that modeling volatility dynamics is more critical for risk accuracy than complex dependence structures for this type of liquid portfolio.
| Model Category | Key Takeaway |
|---|---|
| Filtered Hist. Sim. (FHS) | Most robust performer; successfully captured volatility bursts and tail events. |
| Student-t GARCH | Superior to Gaussian models by accounting for the leptokurtic nature of returns. |
| Copula Methods | Provided better tail-risk estimates at extreme levels (99%), but did not systematically outperform FHS. |
| Backtesting Results | FHS and Student-t GARCH passed validation tests, while simple Historical Simulation failed during high-volatility regimes. |
Conclusion on Copulas: While copulas better model extreme dependence, their marginal contribution is limited compared to proper univariate volatility specification (like GARCH/FHS) in highly liquid markets.
🛠 Tools & Libraries:
- Python (Arch & Copulae): Core engines for GARCH processes and elliptical/archimedean copula fitting.
- Statsmodels: Used for rigorous statistical testing and time-series diagnostics.
- YFinance: Automated extraction of historical market data.
🧠 Techniques:
- Time-Varying Volatility (GARCH)
- Tail Risk Measurement (VaR & Expected Shortfall)
- Multi-variate Joint Distribution Modeling (Copulas)
- Model Validation & Statistical Backtesting