High-frequency trading with fractional Brownian motion

Paolo Guasoni (), Yuliya Mishura () and Miklós Rásonyi ()
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Paolo Guasoni: Dublin City University
Yuliya Mishura: Taras Schevchenko National University of Kyiv
Miklós Rásonyi: Alfréd Rényi Institute of Mathematics

Finance and Stochastics, 2021, vol. 25, issue 2, No 3, 277-310

Abstract: Abstract In the high-frequency limit, conditionally expected increments of fractional Brownian motion converge to a white noise, shedding their dependence on the path history and the forecasting horizon and making dynamic optimisation problems tractable. We find an explicit formula for locally mean–variance optimal strategies and their performance for an asset price that follows fractional Brownian motion. Without trading costs, risk-adjusted profits are linear in the trading horizon and rise asymmetrically as the Hurst exponent departs from Brownian motion, remaining finite as the exponent reaches zero while diverging as it approaches one. Trading costs penalise numerous portfolio updates from short-lived signals, leading to a finite trading frequency, which can be chosen so that the effect of trading costs is arbitrarily small, depending on the required speed of convergence to the high-frequency limit.

Keywords: Fractional Brownian motion; Transaction costs; High frequency; Trading; Mean–variance optimisation; 91G10; 91G80 (search for similar items in EconPapers)
JEL-codes: G11 G12 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s00780-020-00439-y

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