Learning Before Scheduled Events: Prediction Markets, State Prices, and Option Valuation

Scheduled events — referendums, elections, central-bank decisions — resolve at a known date, but the information that determines their outcome arrives gradually beforehand. We measure that arrival directly from traded event probabilities. Event-clock (information) time is defined as the quadratic variation of the log-odds of the traded probability, and records how much outcome-relevant information has arrived, and when. We show how raw state prices from prediction markets are normalized into risk-adjusted event probabilities, and develop realized-variation estimators of the information clock together with truncation, bipower, and largest-move robustness variants and a real-time forecast rule. We derive the exact logistic-normal transition law of the event probability in closed form, which yields analytic expressions for event-conditional moments, exceedance and revision probabilities, at-the-money event option values, effective volatility, and the event share of total variance. The framework links prediction-market prices, state prices, and option valuation within a single set of state variables, and delivers realized event exposures for individual assets. We illustrate the approach on the 2016 Brexit referendum and the 2016 and 2024 U.S. presidential elections.

Working Paper (University of Liechtenstein & Free University of Bozen-Bolzano)