2026/02/28 by Nam Anh Le
Mathematics · #stat.AP #msc:62P20
33 pages, 8 figures, 21 tables. Revised manuscript. Code and replication materials: https://github.com/namanhzz/prediction-market-calibration
arxiv created 2026/08/04 · arxiv updated 2026/08/05
Prediction market prices are often read as probabilities, but this reading requires calibration. Using 353 million trades across 429,000 binary contracts on Kalshi and Polymarket, this paper measures how calibration varies with event domain, time-to-resolution and trade size. A descriptive decomposition of cell-level logistic recalibration slopes explains 87.3% of in-sample variance on Kalshi (71.5% out-of-sample). The most robust pattern is persistent underconfidence in political markets, where prices compress toward 50%; it replicates on Polymarket. Large political trades on Kalshi are associated with further compression, with a calibration-slope gap of roughly one-half that survives market- and event-clustered bootstraps but is not robust on Polymarket. A Bayesian measurement-error model that propagates first-stage uncertainty agrees with these conclusions and indicates that, under conservative event-clustered standard errors, roughly half of the raw slope variation reflects estimation noise. Calibration is therefore conditional: a price's meaning depends on what, when and how much is traded.