VaR-ES-Backtesting-GARCH

Backtesting Value-at-Risk and Expected Shortfall with GARCH-family models (t & skew-t) in R

This project implements and evaluates Value-at-Risk (VaR) and Expected Shortfall (ES) forecasts using GARCH-family models.
The focus is on GARCH(1,1), APARCH(1,1), and EGARCH(1,1) with both t-distribution and skewed t-distribution.
The work was done as part of the course W4451-FEQRM Project – Summer Semester 2025.

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Project Overview

• Data: Daily closing stock prices of a company (2020–2024) from Yahoo Finance.
• Models:
  • GARCH(1,1)
  • APARCH(1,1)
  • EGARCH(1,1)
• Distributions: t and skewed t
• Risk Level: 97.5%
• Backtest: Traffic-light test and violation counts

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Methods

1. Load and clean stock price data (2020–2024).
2. Compute daily log-returns.
3. Fit models on training data, leaving the last 250 observations for testing.
4. Generate one-step rolling forecasts of 97.5% VaR and ES.
5. Backtest forecasts using violation counts and traffic-light zones.
6. Visualize returns vs VaR and ES, marking violations.

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Visualization of VaR and ES Backtests

The figures show daily log-returns (black) with forecasted 97.5% VaR (red dashed) and 97.5% ES (blue dashed).
Violations (returns falling below the thresholds) are highlighted with markers.

Each model-distribution combination has its own plot.
Example below (illustrative):

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Results

• Expected number of violations at 97.5% over 250 days ≈ 6–7.
• Some models under- or over-estimate tail risk.
• Skewed-t distributions often provide a better fit compared to symmetric t.

See summary_backtests.csv for the consolidated results.

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📁 Repository Structure