Volatility & Risk Management (Peru ADRs) — GARCH(1,1)

Quantitative finance project that estimates conditional volatility using a GARCH(1,1) model and computes risk measures (Value at Risk and Expected Shortfall) for internationally traded Peruvian assets (BAP, BVN) using Python.

Methodology

• Daily price download using yfinance (2015–2025)
• Log-return transformation
• Visual evidence of volatility clustering
• GARCH(1,1) estimation with:
  • Normal distribution
  • Student-t distribution (heavy tails)
• 95% VaR and Expected Shortfall estimation
• Backtesting through violation frequency
• Normal vs Student-t comparison (extreme risk)

Key Results

• High volatility persistence (α+β ≈ 0.95)
• Heavy-tailed behavior (ν ≈ 4.3)
• 95% VaR: violation rate close to the theoretical 5%
• Student-t captures extreme losses better than Normal distribution

Tools

Python, yfinance, pandas, numpy, matplotlib, arch, scipy

Outputs

The following files are generated in /data:

• raw_prices.csv
• log_returns.csv
• clustering_volatilidad.png
• var_garch_95.png
• comparacion_modelos.csv
• comparacion_volatilidades.png

How to Run

pip install -r requirements.txt
py main.py

requirements.txt

yfinance
pandas
numpy
matplotlib
arch
scipy