On the Analysis of a Generalised Rough Ait-Sahalia Interest Rate Model

Emmanuel Coffie,Xuerong Mao,Frank Proske

arXiv · Probability

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Abstract

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 an Ait-Sahalia-type interest rate 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.

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