Implied Inflation Distributions and Moments (1Y)

This repository implements a full pipeline to recover risk-neutral one-year inflation distributions and moments from option prices.

The objective is identification and stability, not forecasting.

We compare multiple methods and analyze when higher moments are weakly identified due to limited strike coverage and boundary effects.

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Methods Implemented

1. Breeden–Litzenberger (BL)

• Prices → Density → Moments
• Density recovered via second derivative of call prices: [ f(k) = \frac{1}{B(0,1)} \frac{\partial^2 C(k)}{\partial k^2} ]
• Sensitive to numerical noise (finite differentiation)

2. Kitsul–Wright (KW)

• Operational version of BL
• Local polynomial smoothing before differentiation
• Improves numerical stability

3. Bakshi–Kapadia–Madan (BKM)

• Prices → Moments directly
• No density recovery
• Highly sensitive to truncation and tail coverage

4. Maximum Entropy (MaxEnt)

• Prices → Density → Moments
• Discrete probability grid
• Regularized convex optimization
• Used as a robustness benchmark

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KW Boundary Shutdown Rule

Information window: pi in [-1%, 5%]

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Repository Structure

option_implied_inflation_probability_density_functions/
├─ README.md
├─ requirements.txt
├─ LICENSE
├─ .gitignore
├─ options_implied_inflation_pdf.py
├─ results/
│ ├─ fig/
│ └─ updated_results.csv
├─ report/
│ └─ main.tex
└─ data/
  └─ README_DATA.md

Data (Bloomberg licensing)

Raw data files are sourced from Bloomberg and are therefore not included in this repository.

To reproduce the pipeline, place your own licensed data files in data/.

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Installation

1) Create a virtual environment (recommended)

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

2) Install dependencies

pip install -r requirements.txt

Run the pipeline

python src\options_implied_inflation_pdf.py

Authors

Nam Khanh Nguyen, Rodrigue Mieuzet, Melany Gipsy Moreno, Khrystyna Kateryna Valenia, Katarzyna Pastuszka

Master 2 Finance Technology Data (FTD) Université Paris 1 Panthéon-Sorbonne