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 for Applied Analysis and Stochastics

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 for Applied Analysis and Stochastics ( 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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