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Statistical arbitrage under a fractal price model

Author

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  • Yun Xiang

    (Southwestern University of Finance and Economics)

  • Shijie Deng

    (Georgia Institute of Technology)

Abstract

We investigate a class of statistical arbitrage strategies under the assumption that stock prices are driven by fractional Brownian motions. Specifically, the buy-and-hold with a stop-profit threshold strategies are analysed to demonstrate the existence of statistical arbitrage opportunities. Our analysis establishes the conditions for the considered strategy class to yield statistical arbitrage. The Hurst parameter in the fractional Brownian motion-based asset price model is shown to be a determining factor. The analysis is confirmed by a Monte Carlo simulation study. Furthermore, a modified Thompson sampling method is proposed for optimizing the strategy parameters of the selling-threshold and its growth rate to maximize investment performance.

Suggested Citation

  • Yun Xiang & Shijie Deng, 2024. "Statistical arbitrage under a fractal price model," Annals of Operations Research, Springer, vol. 335(1), pages 425-439, April.
    • Handle: RePEc:spr:annopr:v:335:y:2024:i:1:d:10.1007_s10479-023-05585-y
    DOI: 10.1007/s10479-023-05585-y
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    References listed on IDEAS

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    1. Marco Corazza & A.G. Malliaris & Carla Nardelli, 1997. "Searching for fractal structure in agricultural futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(4), pages 433-473, June.
    2. Binh Do & Robert Faff, 2012. "Are Pairs Trading Profits Robust To Trading Costs?," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 35(2), pages 261-287, June.
    3. Erdinc Akyildirim & Frank J. Fabozzi & Ahmet Goncu & Ahmet Sensoy, 2022. "Statistical arbitrage in jump-diffusion models with compound Poisson processes," Annals of Operations Research, Springer, vol. 313(2), pages 1357-1371, June.
    4. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    5. Hogan, Steve & Jarrow, Robert & Teo, Melvyn & Warachka, Mitch, 2004. "Testing market efficiency using statistical arbitrage with applications to momentum and value strategies," Journal of Financial Economics, Elsevier, vol. 73(3), pages 525-565, September.
    6. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    7. Paolo Guasoni & Yuliya Mishura & Miklós Rásonyi, 2021. "High-frequency trading with fractional Brownian motion," Finance and Stochastics, Springer, vol. 25(2), pages 277-310, April.
    8. Liu, Qiang & Xiang, Yun & Zhao, Yonghong, 2019. "An outperforming investment strategy under fractional Brownian motion," The North American Journal of Economics and Finance, Elsevier, vol. 47(C), pages 505-515.
    9. Daniel Russo & Benjamin Van Roy, 2014. "Learning to Optimize via Posterior Sampling," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 1221-1243, November.
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