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Forecasting with fractional Brownian motion: a financial perspective

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  • Matthieu Garcin

Abstract

The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the non-Markovian nature of the fBm to forecast future states of the process and make statistical arbitrages. We provide new insights into forecasting an fBm, by proposing theoretical formulas for accuracy metrics relevant to a systematic trader, from the hit ratio to the expected gain and risk of a simple strategy. In addition, we answer some key questions about optimizing trading strategies in the fBm framework: Which lagged increments of the fBm, observed in discrete time, are to be considered? If the predicted increment is close to zero, up to which threshold is it more profitable not to invest? We also propose empirical applications on high-frequency FX rates, as well as on realized volatility series, exploring the rough volatility concept in a forecasting perspective.

Suggested Citation

  • Matthieu Garcin, 2022. "Forecasting with fractional Brownian motion: a financial perspective," Quantitative Finance, Taylor & Francis Journals, vol. 22(8), pages 1495-1512, August.
    • Handle: RePEc:taf:quantf:v:22:y:2022:i:8:p:1495-1512
    DOI: 10.1080/14697688.2022.2071758
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    Citations

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    Cited by:

    1. Daniele Angelini & Matthieu Garcin, 2024. "Market information of the fractional stochastic regularity model," Papers 2409.07159, 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. Angelini, Daniele & Bianchi, Sergio, 2023. "Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Xavier Brouty & Matthieu Garcin, 2022. "A statistical test of market efficiency based on information theory," Papers 2208.11976, arXiv.org.
    5. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Papers 2305.13123, arXiv.org.
    6. Yang, Mo & Wang, Ruotong & Zeng, Zixun & Li, Peizhi, 2024. "Improved prediction of global gold prices: An innovative Hurst-reconfiguration-based machine learning approach," Resources Policy, Elsevier, vol. 88(C).
    7. Xavier Brouty & Matthieu Garcin, 2022. "A statistical test of market efficiency based on information theory," Working Papers hal-03760478, HAL.
    8. Matthieu Garcin, 2023. "Complexity measure, kernel density estimation, bandwidth selection, and the efficient market hypothesis," Working Papers hal-04102815, HAL.
    9. Brouty, Xavier & Garcin, Matthieu, 2024. "Fractal properties, information theory, and market efficiency," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).

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