On the analysis of Ait-Sahalia-type model for rough volatility modelling

Coffie, Emmanuel and Mao, Xuerong and Proske, Frank (2024) On the analysis of Ait-Sahalia-type model for rough volatility modelling. Journal of Theoretical Probability, 37 (1). pp. 744-767. ISSN 0894-9840 (https://doi.org/10.1007/s10959-023-01269-2)

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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 a generalised Ait-Sahaliatype 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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