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

Discrete scheduled events such as elections, referendums, and macroeconomic announcements create risk in the prices of financial instruments. Firm-specific event risk can be diversified away, but its systematic component cannot and is therefore priced by the market. We analyze event risk premia in an expected utility framework with a risk-averse representative investor, covering the four cases given by combining deterministic or stochastic conditional event returns with deterministic or stochastic event outcome probabilities. Letting outcome probabilities evolve as investors learn ahead of the event, we show that the real-world probability process is a martingale under P, just as its traded, risk-neutral counterpart is a martingale under Q, so that prediction-market quotes and state prices are linked through the ratio of the two. Combining this structure with the mixture-of-lognormals model yields closed-form solutions for the event risk premium — under both quadratic and power utility — and for option prices, which take the form of a probability-weighted sum of modified Black (1976) components. Applied to event return distributions estimated in previous work, the model produces event risk premia in the range documented in the empirical literature. The model further generates non-convex volatility smiles in the run-up to events: concavity becomes more likely as outcome probabilities approach one half, as the distance between conditional expected event returns widens, and as conditional variances and time to maturity shrink. Bimodality of the risk-neutral density appears to be a necessary, but not a sufficient, condition for concave smiles.

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