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

TL;DR

This paper investigates a generalized interest rate model driven by fractional Brownian motion with Hurst parameter less than 1/2, establishing key theoretical properties like existence, uniqueness, and regularity of solutions.

Contribution

It introduces a novel fractional Brownian motion-driven interest rate model and provides rigorous mathematical analysis of its properties, extending classical models.

Findings

Proved existence and uniqueness of solutions.

Established Malliavin differentiability of solutions.

Analyzed higher moments of the solutions.

Abstract

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.