Modeling Volatility in Prediction Markets

Nowadays, there is a significant experimental evidence of excellent ex-post predictive accuracy in certain types of prediction markets, such as markets for elections. This evidence shows that prediction markets are efficient mechanisms for aggregating information and are more accurate in forecasting events than traditional forecasting methods, such as polls. Interpretation of prediction market prices as probabilities has been extensively studied in the literature, however little attention so far has been given to understanding volatility of prediction market prices. In this paper, we present a model of a prediction market with a binary payoff on a competitive event involving two parties. In our model, each party has some underlying "ability" process that describes its ability to win and evolves as an Ito diffusion. We show that if the prediction market for this event is efficient and accurate, the price of the corresponding contract will also follow a diffusion and its instantaneous volatility is a particular function of the current claim price and its time to expiration. We generalize our results to competitive events involving more than two parties and show that volatilities of prediction market contracts for such events are again functions of the current claim prices and the time to expiration, as well as of several additional parameters (ternary correlations of the underlying Brownian motions). In the experimental section, we validate our model on a set of InTrade prediction markets and show that it is consistent with observed volatilities of contract returns and outperforms the well-known GARCH model in predicting future contract volatility from historical price data. To demonstrate the practical value of our model, we apply it to pricing options on prediction market contracts, such as those recently introduced by InTrade. Other potential applications of this model include detection of significant market moves and improving forecast standard errors.