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

Author

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  • Mark Richard

    (Frankfurt School of Finance and Management, Adickesallee 32–34, 60322 Frankfurt am Main, Germany)

  • Jan Vecer

    (Frankfurt School of Finance and Management, Adickesallee 32–34, 60322 Frankfurt am Main, Germany
    Department of Probability and Mathematical Statistics, Charles University, Sokolovska 83, 18675 Praha 8, Czech Republic)

Abstract

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

Suggested Citation

  • Mark Richard & Jan Vecer, 2021. "Efficiency Testing of Prediction Markets: Martingale Approach, Likelihood Ratio and Bayes Factor Analysis," Risks, MDPI, vol. 9(2), pages 1-20, February.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:2:p:31-:d:490735
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    References listed on IDEAS

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    Cited by:

    1. Navratil, Robert & Taylor, Stephen & Vecer, Jan, 2022. "On the utility maximization of the discrepancy between a perceived and market implied risk neutral distribution," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1215-1229.
    2. Navratil, Robert & Taylor, Stephen & Vecer, Jan, 2021. "On equity market inefficiency during the COVID-19 pandemic," International Review of Financial Analysis, Elsevier, vol. 77(C).

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