UQO Working Papers · WP08 · v1.1
Prediction Markets as Arrow–Debreu Securities: Evidence from Polymarket
State Prices, No-Arbitrage Bounds and Macroeconomic News in Blockchain-Based Contingent Claims
- Year
- 2026
- First release
- October 2026
- Latest revision
- October 2026
- Publication status
- Working paper
Blockchain state prices sum to one, within the spread, and lead nothing
The complete set of claims is priced at 1.017 (Fed) and 1.015 (election), an overround within the half-spreads that declines towards resolution; the implied policy expectation moves 2–5 times more on FOMC and employment days, yet neither leads nor lags Treasuries, equities, the VIX or Bitcoin.
Abstract
Negative-risk events on Polymarket list one binary contract for every outcome of a decision and settle exactly one of them at one dollar, so that their prices are observable analogues of Arrow–Debreu state prices. The paper uses the five-outcome market on the June 2026 FOMC decision (146 daily closes, December 2025 to May 2026) and the seventeen-contract market on the 2024 U.S. presidential election (304 daily closes) to ask how the Arrow–Debreu pricing restrictions fare in a blockchain market. Because spanning is built into the contract design, the testable content is the law of one price for the complete set of claims, whose executable no-arbitrage bounds are derived from the platform's minting and conversion mechanics.
The sum of state prices averages 1.017 (Fed) and 1.015 (election); the overround is statistically positive but of the order of the quoted half-spreads of the low-priced legs, declines steadily towards resolution, reverts within two days, and is bracketed by the bid- and ask-side sums of the order book. It has the wrong sign to be explained by the time value of money, which places the complete set below one. The normalised prices define a risk-neutral distribution over the FOMC decision whose mean, a Polymarket analogue of the futures-implied expected policy change, moves two to five times more, in variance terms, on FOMC and employment-report days than on other days, while weekend trading carries about one third of weekday variance.
Once Polymarket closes are aligned to the U.S. trading calendar and lag orders are chosen by information criteria, daily changes in this measure neither lead nor lag the ten-year Treasury yield, the S&P 500, the VIX or Bitcoin. The paper documents how a one-day misalignment of blockchain time stamps and a minimum-p lag search generated spurious lead–lag findings in an earlier version.
Key findings
146 / 304
daily closes, Fed (5 claims) and election (17)
1.017 / 1.015
mean sum of state prices, Fed and election
5.1 → 0.4 pp
Fed overround, first 30 days to last 30 days
0.999 / 1.004
bid-side and ask-side sums of the order book
4.9×
variance ratio of implied policy change, release days
p > 0.18
all Granger tests, both directions, four markets
Scientific contributions
- Executable no-arbitrage bounds from platform mechanics
- Minting and conversion mechanics imply e^{−rτ} − c ≤ Σ ≤ 1 + c for the complete set; the mean discounted lower bound is 0.989, so the time value of money cannot explain a sum above one.
- The overround is not an arbitrage
- Σ averages 1.0167 (Fed, HAC t = 3.8) and 1.0146 (election), falls from 5.1 to 0.4 percentage points over the Fed market's life, has a half-life of 2.1 days, and the 22 May 2026 order book shows bid and ask sums of 0.999 and 1.004.
- A risk-neutral policy expectation that responds to news
- The implied expected June 2026 policy change moves 1.15 basis points on the 13 scheduled release days against 0.51 on the other 132 (variance ratio 4.9, Brown–Forsythe p = 0.008), and the modal state price moves 5.5 versus 1.4 points; weekends carry about one third of weekday variance.
- No daily lead–lag with traditional markets
- On the U.S. trading-day grid with lag order chosen by AIC/BIC/HQIC and HAC tests, all Granger tests between the Polymarket measure and the 10-year yield, SPY, VIX and Bitcoin have p-values between 0.19 and 0.90; the contemporaneous correlation with the 10-year yield change is 0.26.
- An earlier lead–lag result traced to a calendar error
- The version 1.0 finding that Polymarket led the VIX (p = 0.001) came from labelling 00:00 UTC closes as the following day and selecting lags by minimum p-value; the paper reconciles the two versions explicitly.
Methodology
Methodology (4)
Pricing of the complete set
Daily sums Σ_t, HAC test of the overround, shares within ±0.5/1/2/5 points, discounted bounds from the federal funds rate, AR(1) half-life, ADF and a term-structure regression on time to resolution, with order-book bid, ask and depth sums.
Risk-neutral distribution
Normalised prices q_j = p_j/Σ define the distribution over the five policy states valued at −50, −25, 0, +25 and +50 basis points; its mean and standard deviation give an implied expected policy change and its dispersion.
Announcement-day analysis
Day-0 and cumulative changes for 4 FOMC, 4 CPI and 5 employment releases; release versus other days compared by variance ratios, Brown–Forsythe and one-sided Mann–Whitney tests, and weekend versus weekday variance.
Lead–lag tests
Bivariate Granger tests and a five-variable VAR(1) on the trading-day grid with lag order chosen by AIC, BIC and HQIC, HAC Wald tests and fixed-lag sensitivity; GARCH, GJR and HAR volatility models relegated to an appendix after ARCH-LM fails to reject.
Research data
- Polymarket negative-risk groups
- Daily price histories, order-book snapshot and metadata from the Polymarket Gamma and CLOB APIs for the Fed June 2026 group (event 101772, 5 outcomes, $37.8 million volume, 146 closes) and the 2024 Presidential Election Winner event (903193, 17 contracts, $3.7 billion volume, 304 closes), snapshot of 22 May 2026; closes relabelled to the UTC day they end.
- Macro and market series
- Effective federal funds rate, CPI and unemployment releases from FRED; SPY, VIX, 10-year yield index and BTC-USD from Yahoo Finance, aligned to the U.S. trading calendar (110 common trading days for the Fed sample).
Reproducibility
- scripts/02_revision_analysis.py regenerates every table, figure and quoted number (results/revision_stats.json) offline from the raw snapshot in about 1 minute
- Download and cleaning pipeline in src/ (Polymarket, FRED, Yahoo clients; close-of-day relabelling; AIC lag selection) with a FRED key for the network stage
- Nine LaTeX table fragments and twelve figures generated by script; full LaTeX source of the 44-page paper with 62 verified references
- Appendix C reconciles version 1.0 with version 1.1; pre-revision PDF, review report and changelog kept in docs/
Research artifacts
Version history
| Version | Date | Description | File |
|---|---|---|---|
| v1.1current | October 2026 | Current manuscript as published on www.spboucher.ai (revised edition after the 2026-10-17 scientific review for papers 1–17). | PDF · 44 p. |