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

Emmanuel Coffie,Xuerong Mao,Frank Proske

JOURNAL OF THEORETICAL PROBABILITY（2024）

University of Liverpool | University of Strathclyde | University of Oslo

Cited 2|Views8

Abstract

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 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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Key words

Rough volatility,Malliavin calculus,Fractional Brownian motion,Strong solution,Higher moments

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