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High-frequency trading with fractional Brownian motion

Author

Listed:
  • Paolo Guasoni

    (Dublin City University)

  • Yuliya Mishura

    (Taras Schevchenko National University of Kyiv)

  • Miklós Rásonyi

    (Alfréd Rényi Institute of Mathematics)

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.

Suggested Citation

  • Paolo Guasoni & Yuliya Mishura & Miklós Rásonyi, 2021. "High-frequency trading with fractional Brownian motion," Finance and Stochastics, Springer, vol. 25(2), pages 277-310, April.
    • Handle: RePEc:spr:finsto:v:25:y:2021:i:2:d:10.1007_s00780-020-00439-y
    DOI: 10.1007/s00780-020-00439-y
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Kerstin Lamert & Benjamin R. Auer & Ralf Wunderlich, 2023. "Discretization of continuous-time arbitrage strategies in financial markets with fractional Brownian motion," Papers 2311.15635, arXiv.org.
    2. Xavier Brouty & Matthieu Garcin & Hugo Roccaro, 2024. "Estimation of bid-ask spreads in the presence of serial dependence," Papers 2407.17401, arXiv.org.
    3. Matthieu Garcin, 2021. "Forecasting with fractional Brownian motion: a financial perspective," Papers 2105.09140, arXiv.org, revised Sep 2021.
    4. Minglian Lin & Indranil SenGupta, 2023. "Analysis of optimal portfolio on finite and small-time horizons for a stochastic volatility model with multiple correlated assets," Papers 2302.06778, arXiv.org, revised Dec 2023.
    5. Brouty, Xavier & Garcin, Matthieu, 2024. "Fractal properties, information theory, and market efficiency," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    6. Matthieu Garcin, 2021. "Forecasting with fractional Brownian motion: a financial perspective," Working Papers hal-03230167, HAL.

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    More about this item

    Keywords

    Fractional Brownian motion; Transaction costs; High frequency; Trading; Mean–variance optimisation;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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