  Fractional Brownian motion with the Hurst parameter $H<\frac{1}{2}$ is used
widely, for instance, to describe a 'rough' stochastic volatility process in
finance. In this paper, we examine an Ait-Sahalia-type interest rate model
driven by a fractional Brownian motion with $H<\frac{1}{2}$ 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.
