Trading Fractional Brownian Motion

21 Pages Posted: 22 Jun 2017 Last revised: 22 May 2019

See all articles by Paolo Guasoni

Paolo Guasoni

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

Zsolt Nika

Peter Pazmany Catholic University

Miklos Rasonyi

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

Date Written: November 6, 2018

Abstract

In a market with an asset price described by fractional Brownian motion, which can be traded with temporary nonlinear price impact, we find asymptotically optimal strategies for the maximization of expected terminal wealth. Exploiting the autocorrelation in increments while limiting trading costs, these strategies generate an average terminal wealth that grows with a power of the horizon, the exponent depending on both the Hurst and the price-impact parameters. The resulting Sharpe ratios are bounded, insensitive to the horizon, and asymmetric with respect to the Hurst exponent.
These results extend Gaussian processes with long memory and to a class of self-similar processes.

Keywords: fractional Brownian motion, transaction costs, price impact, trading

JEL Classification: G11

Suggested Citation

Guasoni, Paolo and Nika, Zsolt and Rasonyi, Miklos, Trading Fractional Brownian Motion (November 6, 2018). Available at SSRN: https://ssrn.com/abstract= or http://dx.doi.org/10.2139/ssrn.2991275

Paolo Guasoni (Contact Author)

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

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

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Zsolt Nika

Peter Pazmany Catholic University

Szentkirályi utca 28
Budapest
Hungary

Miklos Rasonyi

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

Realtanoda u 13-15
Budapest
Hungary

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