Nonlinear biases in the roughness of a Fractional Stochastic Regularity Model

A Multifractional Process with Random Exponent (MPRE) is used to model the dynamics of log-prices in a financial market. Under this assumption, we show that the Hurst-Hölder exponent of the MPRE follows the fractional Ornstein–Uhlenbeck process which in the Fractional Stochastic Volatility Model of Comte and Renault (1998) describes the dynamics of the log-volatility. We provide evidence that several biases of the estimation procedures can generate artificial rough volatility in surrogated as well as real financial data. •Modelling log-prices by a MPRE, a Fractional Stochastic Regularity Model is defined.•The Hurst exponent is the same fOU process of the log-volatility in the RFSV model.•We estimate the global Hurst exponent of the fOU process and of its estimated paths.•Using three methods, we find that nonlinear biases can generate spurious roughness.