Investigating the Statistical Properties of the Hurst Exponent Estimator of Rough Volatility Model

Abstract

The aim of this thesis is to provide a characterization of the statistical properties of estimator of the Hurst parameter of the rough stochastic volatility model following fractional Brownian motion with Hurst index H. For this purpose, we perform a simulation experiment for fractional Brownian motion based on the circulant embedding method. Moreover, the study contributes to make a comparison between the Hurst estimator and the memory parameter estimator, d. The results indicate that the Hurst estimator is superior to considered memory estimators, however, in the presence of microstructure noise, it is downward biased.