Statistical arbitrage under a fractal price model

Yun Xiang and Shijie Deng ()
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Yun Xiang: Southwestern University of Finance and Economics
Shijie Deng: Georgia Institute of Technology

Annals of Operations Research, 2024, vol. 335, issue 1, No 16, 425-439

Abstract: 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.

Keywords: Fractional Brownian motion; Statistical arbitrage; Thompson sampling; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-023-05585-y

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