This repository contains the code and paper for the project:

Quantum-Entropic Martingale Transport for Robust Model-Free Derivative Pricing

PDF: Quantum-Entropic-MOT.pdf
Code: manage.py

Most market models (Black–Scholes, Heston, SABR) rely on fragile assumptions and unstable calibrations.
This project introduces a quantum-inspired, entropically-regularised variant of Martingale Optimal Transport (MOT) to deliver:

• Model-free no-arbitrage bounds for forward-start and European-style derivatives.
• Worst-case Greeks for conservative hedging and risk management.
• Stress testing through perturbed distributions.

The framework is scalable, stable, and integrates naturally with volatility smile workflows.

.
├─ Quantum-Entropic-MOT.pdf     # Paper (final version)
├─ manage.py                    # Python script to reproduce figures & data
├─ requirements.txt             # Python dependencies
└─ outputs/                     # Generated outputs (after running the script)
   ├─ fig_bounds_vs_epsilon.pdf
   ├─ fig_qeot_sensitivity_eps.pdf
   ├─ fig_spx_market_bands.pdf
   ├─ fig_tail_stress_asymmetry.pdf
   ├─ bounds_vs_epsilon.csv
   ├─ bands_vs_alpha.csv
   ├─ stress_results.csv
   └─ manifest.json

1. Clone the repo:

   git clone https://github.com/<your-username>/QEOT-MOT.git
   cd QEOT-MOT

2. Install dependencies:

   pip install -r requirements.txt

3. Run the full pipeline:

   python manage.py --generate-all --outdir outputs

4. All figures and CSVs will appear in the outputs/ folder.
   You can then recompile the LaTeX paper with main.tex if needed.

• Forward-start bounds vs ε
• Bands vs strike multiple (α)
• ε-sensitivity (QEOT / Entropic MOT)
• Asymmetric widening under right-tail stress

MIT License – feel free to use, modify, and share with attribution.

Piet, Elliot. Quantum-Entropic Martingale Transport for Robust Model-Free Derivative Pricing, 2025.