A Multi-Step Binomial Model for Prediction Markets

This short note adapts a multi-period binomial model for asset pricing under heterogeneous beliefs developed by He and Shi in July 2010 to the case of prediction markets thereby generalizing known results on the formation of prediction market prices. In this setup, the prices of the contracts are given as conditional expectations of the pay-o off event conditional on the information available thus emulating the risk-neutral valuation of contingent claims. The probability measure of the expectation operator is the measure determined by the market and given as a wealth-weighted average of agents' beliefs. The class of discrete random processes considered here also limits the continuous-time stochastic processes usually made in intertemporal models of prediction markets and our work sheds light on typical assumptions made in the literature