Overview

This repository is the reproducible research package for the working paper:

Value at Risk versus Conditional Value at Risk: A Rigorous Framework for Measuring Extreme Tail Risk and Regulatory Compliance

It studies VaR, CVaR, and Expected Shortfall through mathematical analysis, Monte Carlo simulation, robustness checks, backtesting, and regulatory interpretation.

What is included

• empirical and closed-form VaR/CVaR implementations;
• the two-defaultable-bond counterexample to VaR subadditivity;
• Gaussian and standardized Student-t loss models;
• convergence and tail-thickness sensitivity studies;
• VaR exception and Kupiec backtesting utilities;
• a reproducible Jupyter notebook;
• generated CSV result tables and publication-ready figures;
• a LaTeX working paper;
• automated tests and GitHub Actions CI;
• citation, authorship, license, and reproducibility metadata.

Repository structure

asr-var-cvar-tail-risk/
├── .github/workflows/python-ci.yml
├── docs/METHODOLOGY.md
├── figures/
├── notebooks/var_cvar_reproduction.ipynb
├── paper/
│   ├── main.tex
│   ├── references.bib
│   └── README.md
├── results/
├── scripts/run_analysis.py
├── src/asr_tail_risk/
│   ├── __init__.py
│   ├── backtesting.py
│   ├── models.py
│   ├── plotting.py
│   ├── risk_measures.py
│   └── simulation.py
├── tests/
├── AUTHORS.md
├── CHANGELOG.md
├── CITATION.cff
├── LICENSE
├── Makefile
├── README.md
├── REPRODUCIBILITY.md
├── pyproject.toml
└── requirements.txt

Installation

git clone https://github.com/Alpha-Stochastic-Research/asr-var-cvar-tail-risk.git
cd asr-var-cvar-tail-risk

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

python -m pip install --upgrade pip
pip install -e ".[dev]"

Reproduce everything

python scripts/run_analysis.py
pytest -q

Or:

make reproduce

The analysis writes tables to results/ and figures to figures/.

Baseline experiment

The Student-t model is rescaled so that its unconditional volatility matches the Gaussian benchmark.

Package usage

from asr.risk.tail import (
    empirical_var,
    empirical_cvar,
    gaussian_var,
    gaussian_cvar,
    simulate_student_t_losses,
)

losses = simulate_student_t_losses(
    n_paths=200_000,
    notional=10_000_000,
    volatility=0.012,
    degrees_of_freedom=4,
    seed=42,
)

var_99 = empirical_var(losses, 0.99)
cvar_99 = empirical_cvar(losses, 0.99)

Python Import Namespace

The package is distributed under the project name:

asr-var-cvar-tail-risk

The recommended Python import namespace is:

from asr.risk.tail import TailRiskConfig

The legacy namespace remains available for backward compatibility:

from asr_tail_risk import TailRiskConfig

New applications, notebooks, and research scripts should use asr.risk.tail.

Working paper

Compile from the repository root:

cd paper
pdflatex main.tex
bibtex main
pdflatex main.tex
pdflatex main.tex

Citation

Citation metadata are provided in CITATION.cff.

License

MIT License. See LICENSE.

Contact

Alpha Stochastic Research
https://asr-lab.online
research@asr-lab.online