Efficiency Testing of Prediction Markets: Martingale Approach, Likelihood Ratio and Bayes Factor Analysis

This paper studies efficient market hypothesis in prediction markets and the results are illustrated for in-play football betting using quoted odds English Premier League. Our analysis is based on martingale property, where last probability should be best predictor of outcome all previous quotes statistically insignificant. We use regression to test significance both time setup spatial stopping times, when probabilities reach certain bounds. The main contribution this show how a potentially different distributional opinion violation efficiency can monetized by optimal trading, agent maximizes logarithmic utility function. In particular, trader realize trading profit that corresponds likelihood ratio situation one maker taker, or Bayes factor two more takers.