Are Prediction Market Prices Probabilities?

Polymarket processed $3.5 billion during the 2024 U.S. election. Kalshi won a landmark CFTC ruling. Prediction markets are now a real asset class — but nobody has a pricing model for them.

Equity options have Black-Scholes. Credit markets have Merton. Prediction markets have… nothing. Prices are formed on order books, but no theory connects them to a stochastic process, no implied volatility surface exists, and there is no formal way to separate probability from risk premium in an observed price.

This matters because prediction market contracts are binary options in incomplete markets. You can't delta-hedge a prediction market contract — the "underlying" is the event itself. A geopolitical outcome, a Fed decision, a basketball game. There is no asset to trade as a hedge. So the observed price necessarily embeds both the probability of the event and a risk premium that no-arbitrage reasoning alone cannot separate.

The Decomposition

I propose a single equation that separates the two:

Here $p^*$ is the physical probability of the event, $p^{\text{mkt}}$ is the observed market price, $\Phi$ is the standard normal CDF, and $\lambda$ is the pricing wedge — how much the market overcharges relative to the true probability.

This is the Wang (2000) transform, originally developed for catastrophe bond pricing. I apply it to prediction markets. The key insight: when $\lambda > 0$, longshots (low-probability events) are proportionally more overpriced than favorites — generating the favorite-longshot bias as a direct mathematical consequence.

Try It Yourself

What the Data Shows

I calibrate $\lambda$ on 290,730 resolved contracts from six platforms spanning 2015–2026:

Every real-money platform shows a positive pricing wedge. Manifold — where participants trade with play-money tokens — shows the opposite sign: the estimated wedge flips direction rather than merely attenuating. The pairwise differences are large: Polymarket − Manifold ≈ 0.38, Kalshi − Manifold ≈ 0.40, with implied z-statistics above 11.

The Pricing Wedge Decays Over Time

Perhaps the most striking finding: the pricing wedge is not constant. It decays as information arrives over the contract's lifetime.

What Drives the Cross-Section?

A one-stage hierarchical model reveals three systematic determinants of the pricing wedge:

Volume (−): Higher-liquidity markets exhibit smaller wedges. In the highest-volume tier (>$10K), $\hat{\lambda} \approx 0$ — competitive trading eliminates the wedge entirely.

Duration (+): Longer-duration contracts carry proportionally larger wedges, establishing a term structure of event risk.

Extremity (−): Contracts near 50% (maximum uncertainty) carry the largest wedges. As outcomes become more predictable, the wedge shrinks.

Why This Matters

For traders: The Wang correction extracts risk-adjusted probabilities from market prices. A 10% market price implies a physical probability of ~8.4%, not 10%. The framework provides a principled fair-value signal.

For regulators: As the CFTC and SEC debate whether event contracts are financial instruments, understanding the risk premium structure of these markets is essential for investor protection and market design.

For researchers: The framework connects prediction markets to three established literatures — distortion risk measures (Wang, 2000), incomplete market pricing (Harrison and Pliska, 1983), and the interpretation of prediction market prices (Manski, 2006).