It takes all sorts: the complexity of prediction markets

Prediction markets represent a great tool to harness the wisdom of the crowd and, for this reason, they are used to provide accurate forecasts on great variety of events. However, current models of prediction markets do not capture their full complexity, and fail to give satisfactory explanations of the price formation process and mispricing anomalies. This thesis consists of six separate, yet interconnected papers that address these gaps. The first three papers analyse the favourite-longshot bias, a well known empirical regularity whereby contracts (or bets) on likely events are underpriced, whereas contracts on unlikely events are overpriced. The favourite-longshot bias has been widely observed especially in sports betting markets but, in contrast with other pricing anomalies, it did not disappear over time. In the first paper, we propose the first model that can explain the favourite-longshot bias and other related phenomena in different contexts. To achieve this, we introduce an agent-model in which market participants possess heterogeneous beliefs and risk attitudes, and find that such a model can accurately explain betting markets mispricing. Moreover, we shed new light on the role bookmakers have in generating mispricing, by considering two different strategies bookmakers can adopt to set prices and show that, in contrast to previous results, bookmakers are more likely to be risk minimisers (i.e., balancing the books only depending on demand) than profit maximisers. The second paper builds on the heterogeneous agents model to investigate the impact of transaction costs on mispricing. Our results suggest that transaction costs alone cannot create mispricing, as suggested by previous work, but significantly amplify its magnitude if mispricing exists already. In the third paper, we provide an analysis of the favourite-longshot bias in political prediction market exchanges, and characterise its temporal behaviour. We find that, on average, mispricing is negatively correlated with duration, i.e., the longer the market, the smaller the favourite-lonsghot bias, but, surprisingly, we find that duration is strongly, and positively correlated to the magnitude of the favourite-longshot bias in the last days of trading, and argue that this is caused by herding dynamics. The second part of the thesis continues the analysis of prediction market exchanges. Specifically, the fourth and fifth paper provide a comprehensive list of empirical regularities (or stylised facts) that we find in prediction market. This list comprises stylised facts on price changes, volume, and calendar effects. Overall, we find that prediction markets behave differently than financial markets, but share some common characteristics, especially regarding price changes, with emerging financial markets. In the sixth and last paper, we build on this work to introduce a model that can replicate the statistical properties of prediction markets. To achieve this, we propose a model in which agents belong to a social network, and can interact with each others by exchanging their opinions about the probability of a specific event to occur. We find that such a model is particularly suitable to explain prediction markets dynamics, and that it qualitatively reproduces the empirical properties of price changes even in the worst case scenario, suggesting strong robustness.