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Long versus short time scales: the rough dilemma and beyond

Author

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  • Matthieu Garcin

    (Léonard de Vinci Pôle Universitaire)

  • Martino Grasselli

    (Léonard de Vinci Pôle Universitaire
    University of Padova)

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.

Suggested Citation

  • Matthieu Garcin & Martino Grasselli, 2022. "Long versus short time scales: the rough dilemma and beyond," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 257-278, June.
    • Handle: RePEc:spr:decfin:v:45:y:2022:i:1:d:10.1007_s10203-021-00358-3
    DOI: 10.1007/s10203-021-00358-3
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    Cited by:

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    4. Daniel dos Santos Baptista & Nuno M. Brites & Alfredo D. Egídio dos Reis, 2023. "Stochastic differential equations death rates models: the Portuguese case," Working Papers REM 2023/0268, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.

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