On the analysis of Ait-Sahalia-type model for rough volatility modelling

Fractional Brownian motion with the Hurst parameter H < 1 2 is used widely, for instance, to describe a ’rough’ stochastic volatility process in finance. In this paper, we examine a generalised Ait-Sahaliatype model driven by a fractional Brownian motion with H < 1 2 and establish theoretical properties such as an existence-and-uniqueness theorem, regularity in the sense of Malliavin differentiability and higher moments of the strong solutions