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Forecasting with fractional Brownian motion: a financial perspective

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  • Matthieu Garcin

    (Research Center - Léonard de Vinci Pôle Universitaire - De Vinci Research Center)

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, 2021. "Forecasting with fractional Brownian motion: a financial perspective," Working Papers hal-03230167, HAL.
    • Handle: RePEc:hal:wpaper:hal-03230167
    Note: View the original document on HAL open archive server: https://hal.science/hal-03230167v3
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    References listed on IDEAS

    as
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    Keywords

    rough volatility; foreign-exchange rates; fractional Brownian motion; Hurst exponent; systematic trading;
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