Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 23 (2018), paper no. 61, 12 pp.
Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint
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.
Electron. Commun. Probab., Volume 23 (2018), paper no. 61, 12 pp.
Received: 1 November 2017
Accepted: 26 July 2018
First available in Project Euclid: 12 September 2018
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G22: Fractional processes, including fractional Brownian motion 60G15: Gaussian processes 60G57: Random measures
Secondary: 60G18: Self-similar processes 28A80: Fractals [See also 37Fxx]
Neuman, Eyal; Rosenbaum, Mathieu. Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint. Electron. Commun. Probab. 23 (2018), paper no. 61, 12 pp. doi:10.1214/18-ECP158. https://projecteuclid.org/euclid.ecp/1536718014