Polymarket-implied volatility vs what happened

An Up or Down price is a probability. Our pricer turns a spot, a price to beat, the time left and a volatility σ into that probability — P(Up) = 1 − Φ(K/(σ·√V)), with K the log-distance to the price to beat and V the effective time (the last 40 seconds drop out of a 60-second TWAP). Run backwards, the same formula turns the order-book mid into the σ the price embeds: a binary-option implied volatility. We did that at mid-window for every graded window of 12 Polymarket crypto markets, Aug 18 – Nov 1, 2026 (75 nights), and kept the 54,375 of 121,443 windows whose mid sat in 15–45% or 55–85%: near 50¢ the inversion is unstable, near 0 or 1 it is meaningless. The first question is the one whose answer does not depend on the law we invert through: how much variance did the price announce for the rest of the window, and how much then happened?

On Bitcoin 5-minute, Bitcoin 15-minute, Ethereum 5-minute, Ethereum 15-minute, the variance implied at mid-window for the remaining half (V-weighted) was 1.00 × the variance that then happened (95% CI 0.96–1.04); 1.01 × the variance that then happened (95% CI 0.91–1.11); 0.95 × the variance that then happened (95% CI 0.92–0.99); 0.90 × the variance that then happened (95% CI 0.80–1.01). The interval contains 1 on 3 of 4; every figure sits within 10% of 1. On the two halves of the period: 1.01 / 0.98 (Bitcoin 5-minute), 0.99 / 1.06 (Bitcoin 15-minute), 0.97 / 0.94 (Ethereum 5-minute), 0.83 / 1.02 (Ethereum 15-minute).

Two controls behind this figure. First, the resolution series (Chainlink 60-second TWAP) and the model's 1-minute Binance candles measure the same variance: over all windows, realized-over-the-window divided by the root-mean-square of the model's σ is 0.99, 0.99, 0.98, 0.98 on the markets with precise levels. Second, the kept windows are those with a large first-half move; their second half realized more than the trailing estimate (33.4% against 27.8% on Bitcoin 5-minute), which is what volatility clustering predicts — the comparison is on those windows, not on an average night. Only the inversion step uses a law: under the Student-t inversion the same ratio reads 1.29, 1.31, 1.23, 1.16, above the normal reading by construction of that law.

Through the normal law, the implied σ is below the trailing realized σ on all 12 markets: 0.80 to 0.94 × (medians per window, bootstrap 95% CIs of ±0.02 at most). Through the Student-t law (ν = 4) that our model also publishes, the same mids read 1.02 to 1.22 × — at or above realized on every market. Nothing in the data changed between the two readings; only the shape of the law did. A renormalized t is more concentrated at the centre, so the same probability needs a larger σ: 1.33 × at 44%, 1.23 × at 15%.

So "does a Polymarket price embed more or less movement than realized?" has no law-free answer at the level of σ; the variance ratio above is the figure to read first, and these two readings are shown as a method detail.

Cut into two halves of equal nights, the normal-inversion ratio keeps its side of 1 on 12 of 12 markets; the largest move between halves is 0.04. By hour of the day (UTC, window open) the ratio differs between hours on 12 of 12 markets (Kruskal–Wallis, p < 0.001): lowest around 2:00, 15:00, 15:00, highest around 13:00, 0:00, 13:00. The per-asset pages carry the profiles.

One minute before the close the same reading keeps only 3% to 16% of windows (most prices sit at 0 or 1 by then) and is not published.