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In this paper, the estimators for the Hurst parameter and diffusion parameter of a Vasicek model driven by fractional Brownian motion are studied, where the observations are in discrete time. Asymptotic properties of these estimators are proved. Using our methods, the smoothness of volatility process of main financial markets is evaluated, corresponding interval estimations are constructed. Our results imply the existence of roughness phenomenon in volatility process.

Calibrating fractional Vasicek model