# 🎯 Prediction Markets as Arrow–Debreu Securities: Evidence from Polymarket **UQO Working Paper No. 8** — *Price Discovery, Market Completeness, and Information Aggregation in Blockchain-Based State-Contingent Claims* [-b31b1b?logo=latex&logoColor=white)](paper/main.pdf) [](pyproject.toml) [](data/raw/README.md) [](scripts/) [](https://uqo.ca) [](mailto:simon-pierre.boucher@uqo.ca) > **TL;DR** — Polymarket binary contracts are modelled as Arrow–Debreu state-contingent claims. On the Fed June 2026 rate-decision neg-risk group (five mutually exclusive outcomes) and the 2024 U.S. Presidential Election markets, state prices sum to **1.02 on average** (146 obs., mean deviation 0.025) with no persistent arbitrage; prediction-market prices move **15–45 minutes ahead** of Treasury futures around FOMC and CPI releases; and Roll spreads / Amihud ratios of high-profile contracts rival those of established markets. Decentralized prediction markets behave as effective Arrow–Debreu economies. --- ## 📌 Status | Item | Value | |---|---| | Version | 1.0 (May 2026) | | SSRN | not yet submitted | | Journal | — | | Code & data | reproducible from `scripts/run_analysis.py` (public APIs; FRED key required) | ## 🎯 What this paper does The paper asks whether blockchain prediction markets satisfy the textbook properties of complete Arrow–Debreu markets: (i) completeness and no-arbitrage — do state prices of mutually exclusive outcomes sum to the discount factor and stay positive? (ii) price discovery — do state prices incorporate macro news before conventional markets? (iii) microstructure quality — are these contracts liquid enough to be used as state-contingent claims? ``` Σ_s π_s = 1/(1+r_f) (completeness) π_s > 0 ∀s (no arbitrage) ``` Tests combine completeness and arbitrage-violation statistics, risk-neutral densities and moments, event studies around FOMC/CPI announcements, Hasbrouck information shares, VAR/Granger causality between Polymarket and Treasury futures, and GARCH/HAR-RV volatility models. ## 🏆 Headline results | Object | Estimate | |---|---| | Mean sum of state prices (Fed neg-risk group) | 1.0205 (sd 0.053, n = 146) | | Mean deviation from unity | 0.0248; max 0.570; all state prices positive | | Lead of Polymarket over Treasury futures around FOMC/CPI | 15–45 minutes | | Liquidity (Roll spread, Amihud) of high-profile contracts | comparable to established markets | ## 🗂 Repository layout ``` polymarket-arrow-debreu/ ├── data/ │ ├── raw/ # Polymarket / FRED / Yahoo snapshots (see data/raw/README.md) — not committed │ └── processed/ # cleaned parquet panels (committed) ├── src/ │ ├── config.py # paths, API endpoints, market registry, event dates │ ├── api/ # polymarket.py, fred.py, yahoo.py, runner.py │ ├── cleaning/ # polymarket_cleaner, macro_cleaner, yahoo_cleaner │ ├── features/ # engineering.py, event_windows.py │ ├── models/ # arrow_debreu, event_study, price_discovery, liquidity, volatility │ └── plots/ # figures.py, tables.py, style.py ├── scripts/ │ └── run_analysis.py # master pipeline: data → cleaning → models → figures/tables ├── results/tables/ # table1…table8 (.tex fragments input by the paper) ├── figures/ # fig1…fig12 (PDF/PNG) └── paper/ # main.tex + sections/ + appendix/ + references.bib → main.pdf ``` ## 🚀 Quick start ```bash python3 -m pip install -e . # dependencies from pyproject.toml cp .env.example .env # set FRED_API_KEY python3 scripts/run_analysis.py # --skip-data / --skip-models / --skip-paper cd paper && make # latexmk → main.pdf ``` ## 🗃 Data Minute-level price histories, order books and metadata for the Fed June 2026 rate-decision markets (event 101772, 5 outcomes), four closed Fed markets and the 2024 Presidential Election markets (Trump / Harris) from the Polymarket Gamma and CLOB APIs; fed funds rate, CPI and unemployment from FRED; Treasury futures and benchmarks from Yahoo Finance. Snapshot 2026-05-22. See `data/raw/README.md`. ## 🔬 Methodology 1. **Completeness & no-arbitrage** — sum of state prices, positivity, implied discount factor, arbitrage-violation detection (`src/models/arrow_debreu.py`). 2. **Risk-neutral density & moments** extracted from the neg-risk group. 3. **Event studies** around FOMC and CPI releases with cumulative abnormal state-price responses (`event_study.py`). 4. **Price discovery** — Hasbrouck information shares, VAR and Granger causality vs Treasury futures (`price_discovery.py`). 5. **Liquidity** — Roll spreads, Amihud illiquidity (`liquidity.py`). 6. **Volatility** — realized measures, GARCH and HAR-RV (`volatility.py`). ## 🖼 Figures & tables inventory | Figure | Content | |---|---| | `fig1_state_prices` | state-price dynamics, Fed June 2026 group | | `fig2_completeness_test` | sum of state prices over time | | `fig3_risk_neutral_density` | implied risk-neutral density | | `fig5_event_study_cars` | cumulative abnormal responses around FOMC/CPI | | `fig7_granger_heatmap` | Granger-causality matrix | | `fig9_volatility` | realized volatility measures | | `fig10_liquidity` | Roll spread and Amihud ratios | | `fig11_election_case_study` | 2024 election markets | | `fig12_arbitrage_violations` | arbitrage-violation episodes | Tables (`results/tables/`): descriptive statistics, summary statistics, completeness tests, event study, Granger, VAR, GARCH, HAR-RV. ## ⚠️ Limitations - Two event families (one Fed neg-risk group, one election) — a small set of high-profile markets. - Polymarket order-book snapshots are point-in-time; depth over the full sample is not observed. - Price-discovery leads are measured at the minute frequency on days with scheduled announcements only. ## 📝 Citation ```bibtex @techreport{boucher2026polymarket, author = {Boucher, Simon-Pierre}, title = {Prediction Markets as Arrow--Debreu Securities: Evidence from Polymarket}, institution = {Universit\'e du Qu\'ebec en Outaouais, D\'epartement des sciences administratives}, type = {Working Paper}, number = {8}, year = {2026}, month = {May} } ``` ## 👤 Author & contact **Simon-Pierre Boucher** — Département des sciences administratives, Université du Québec en Outaouais (UQO), Gatineau, QC. 📧 [simon-pierre.boucher@uqo.ca](mailto:simon-pierre.boucher@uqo.ca) ## 🗒 Notes - Harmonisation 2026-10-17: `tables/` moved to `results/tables/` (paths updated in `src/config.py` and the paper), `run_analysis.py` moved to `scripts/`, empty `logs/`/`notebooks/` removed; `fig5_event_study_cars` is included as PNG (the PDF export was missing).