On the Analysis of Ait-Sahalia-Type Model for Rough Volatility Modelling

Fractional Brownian motion with Hurst parameter H < 1/2 is used widely, for instance, to describe ' rough ' volatility data in finance. In this paper, we examine a generalised Ait-Sahalia-type model driven by a fractional Brownian motionwith 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.