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Stochastic Arbitrage Opportunities: Set Estimation and Statistical Testing

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  • Stelios Arvanitis

    (Department of Economics, Athens University of Economics and Business, 104 34 Athens, Greece)

  • Thierry Post

    (Graduate School of Business, Nazarbayev University, Astana 010000, Kazakhstan)

Abstract

We provide a formal statistical theory of consistent estimation of the set of all arbitrage portfolios that meet the description of being a stochastic arbitrage opportunity. Two empirical likelihood ratio tests are developed: one for the null that a given arbitrage portfolio is qualified, and another for the alternative that the portfolio is not qualified. Apart from considering generalized concepts and hypotheses based on multiple host portfolios, the statistical assumption framework is also more general than in earlier studies that focused on special cases with a single benchmark portfolio. Various extensions and generalizations of the theory are discussed. A Monte Carlo simulation study shows promising statistical size and power properties for testing the null, for representative data dimensions. The results of an empirical application illustrate the importance of selecting a proper blocking structure and moment estimation method.

Suggested Citation

  • Stelios Arvanitis & Thierry Post, 2024. "Stochastic Arbitrage Opportunities: Set Estimation and Statistical Testing," Mathematics, MDPI, vol. 12(4), pages 1-19, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:608-:d:1341021
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    References listed on IDEAS

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    10. Arvanitis, Stelios & Post, Thierry & Potì, Valerio & Karabati, Selcuk, 2021. "Nonparametric tests for Optimal Predictive Ability," International Journal of Forecasting, Elsevier, vol. 37(2), pages 881-898.
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