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arXiv · 1711.00427

Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint

Eyal Neuman·Mathieu Rosenbaum
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Abstract

Rough volatility models are becoming increasingly popular in quantitative finance. In this framework, one considers that the behavior of the log-volatility process of a financial asset is close to that of a fractional Brownian motion with Hurst parameter around 0.1. Motivated by this, we wish to define a natural and relevant limit for the fractional Brownian motion when $H$ goes to zero. We show that once properly normalized, the fractional Brownian motion converges to a Gaussian random distribution which is very close to a log-correlated random field.

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Eyal Neuman, Mathieu Rosenbaum. 2017-11-01. Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint. https://arxiv.org/abs/1711.00427

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