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.
Citation
Eyal Neuman. Mathieu Rosenbaum. "Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint." Electron. Commun. Probab. 23 1 - 12, 2018. https://doi.org/10.1214/18-ECP158
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