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Long vs Short Time Scales: the Rough Dilemma and Beyond

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  • Matthieu Garcin
  • Martino Grasselli

Abstract

Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in the log-log plots of the second moments of realized variance increments against lag which exhibit some convexity in addition to the roughness and stationarity of the volatility. The very low perceived Hurst exponents at small scales is consistent with the rough framework, while the higher perceived Hurst exponents for larger scales leads to a nonlinear behavior of the log-log plot that has not been described by models introduced so far.

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  • Matthieu Garcin & Martino Grasselli, 2020. "Long vs Short Time Scales: the Rough Dilemma and Beyond," Papers 2008.07822, arXiv.org, revised Nov 2021.
    • Handle: RePEc:arx:papers:2008.07822
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    Cited by:

    1. Matthieu Garcin, 2021. "Forecasting with fractional Brownian motion: a financial perspective," Working Papers hal-03230167, HAL.
    2. Matthieu Garcin, 2021. "Forecasting with fractional Brownian motion: a financial perspective," Papers 2105.09140, arXiv.org, revised Sep 2021.

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