Log-Modulated Rough Stochastic Volatility Models

28 Pages Posted: 10 Aug 2020 Last revised: 18 Jan 2021

See all articles by Christian Bayer

Christian Bayer

Weierstrass Institute

Fabian Harang

affiliation not provided to SSRN

Paolo Pigato

University of Rome Tor Vergata - Department of Economics and Finance

Date Written: August 7, 2020

Abstract

We propose a new class of rough stochastic volatility models obtained by modulating the power-law kernel defining the fractional Brownian motion (fBm) by a logarithmic term, such that the kernel retains square integrability even in the limit case of vanishing Hurst index H. The so-obtained log-modulated fractional Brownian motion (log-fBm) is a continuous Gaussian process even for H = 0. As a consequence, the resulting super-rough stochastic volatility models can be analysed over the whole range 0 <= H < 1/2 without the need of further normalization. We obtain skew asymptotics of the form log(1/T)^(-p)T^(H-1/2) as T -> 0, H >= 0, so no flattening of the skew occurs as H -> 0.

Keywords: Rough Volatility Models, Stochastic Volatility, Rough Bergomi Model, Implied Skew, Fractional Brownian Motion, Log Brownian Motion

JEL Classification: G12

Suggested Citation

Bayer, Christian and Harang, Fabian and Pigato, Paolo, Log-Modulated Rough Stochastic Volatility Models (August 7, 2020). Available at SSRN: https://ssrn.com/abstract=3668973 or http://dx.doi.org/10.2139/ssrn.3668973

Christian Bayer

Weierstrass Institute ( email )

Berlin
Germany

Fabian Harang

affiliation not provided to SSRN

Paolo Pigato (Contact Author)

University of Rome Tor Vergata - Department of Economics and Finance

Via Columbia 2
Rome, Rome 00123
Italy

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