High-Frequency Trading with Fractional Brownian Motion

26 Pages Posted: 16 Aug 2019

See all articles by Paolo Guasoni

Paolo Guasoni

Boston University - Department of Mathematics and Statistics; Dublin City University - School of Mathematical Sciences

Yuliya Mishura

Taras Shevchenko National University of Kyiv

Miklos Rasonyi

Hungarian Academy of Sciences (HAS) - Alfréd Rényi Institute of Mathematics

Date Written: August 13, 2019

Abstract

In the high-frequency limit, conditional 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 optimization 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 penalize 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

JEL Classification: G11

Suggested Citation

Guasoni, Paolo and Mishura, Yuliya and Rasonyi, Miklos, High-Frequency Trading with Fractional Brownian Motion (August 13, 2019). Available at SSRN: https://ssrn.com/abstract=3436811 or http://dx.doi.org/10.2139/ssrn.3436811

Paolo Guasoni (Contact Author)

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

Yuliya Mishura

Taras Shevchenko National University of Kyiv ( email )

вул. Володимирська, 60
Kyiv, 01601
Ukraine

Miklos Rasonyi

Hungarian Academy of Sciences (HAS) - Alfréd Rényi Institute of Mathematics

Realtanoda u 13-15
Budapest
Hungary

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