Long versus short time scales: the rough dilemma and beyond

Matthieu Garcin () and Martino Grasselli ()
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Matthieu Garcin: Léonard de Vinci Pôle Universitaire
Martino Grasselli: Léonard de Vinci Pôle Universitaire

Decisions in Economics and Finance, 2022, vol. 45, issue 1, No 10, 257-278

Abstract: 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 are consistent with the rough framework, while the higher perceived Hurst exponents for larger scales lead to a nonlinear behaviour of the log–log plot that has not been described by models introduced so far.

Keywords: Fractional Brownian motion; Rough volatility; Realized variance; Time series; Intra-day data; 60F10; 91G99; 91B25 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10203-021-00358-3

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