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Stochastic Arbitrage Opportunities: Set Estimation and Statistical Testing

Author

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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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    1. Russell Davidson & Jean-Yves Duclos, 2013. "Testing for Restricted Stochastic Dominance," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 84-125, January.
    2. El Ghouch, Anouar & Van Keilegom, Ingrid & McKeague, Ian W., 2011. "Empirical Likelihood Confidence Intervals For Dependent Duration Data," Econometric Theory, Cambridge University Press, vol. 27(1), pages 178-198, February.
    3. Daniel J. Nordman & Helle Bunzel & Soumendra N. Lahiri, 2012. "A Non-standard Empirical Likelihood for Time Series," CREATES Research Papers 2012-55, Department of Economics and Business Economics, Aarhus University.
    4. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
    5. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    6. 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.
    7. Oleg Bondarenko, 2003. "Statistical Arbitrage and Securities Prices," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 875-919, July.
    8. El Ghouch, Anouar & Van Keilegom, Ingrid & McKeague, Ian W., 2011. "Empirical likelihood confidence intervals for dependent duration data," LIDAM Reprints ISBA 2011006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 735-765.
    10. Thierry Post, 2017. "Empirical Tests for Stochastic Dominance Optimality," Review of Finance, European Finance Association, vol. 21(2), pages 793-810.
    11. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    12. Timo Kuosmanen, 2004. "Efficient Diversification According to Stochastic Dominance Criteria," Management Science, INFORMS, vol. 50(10), pages 1390-1406, October.
    13. Thierry Post & Valerio Potì, 2017. "Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood," Management Science, INFORMS, vol. 63(1), pages 153-165, January.
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