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Statistical arbitrage under a fractal price model

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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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    Cited by:

    1. Kerstin Lamert & Benjamin R. Auer & Ralf Wunderlich, 2025. "Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 101(2), pages 163-218, April.

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