Volatility Options in Rough Volatility Models

29 Pages Posted: 16 Feb 2018  

Blanka Horvath

ETH Zurich - Department of Mathematics

Antoine Jacquier

Imperial College London

Peter Tankov

Ecole Polytechnique, Paris

Date Written: February 5, 2018

Abstract

We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where log-volatility follows a Gaussian Volterra process. While providing a good fit for European options, these models are unable to reproduce the VIX option smile observed in the market, and are thus not suitable for VIX products. To accommodate these, we introduce the class of modulated Volterra processes, and show that they successfully capture the VIX smile.

Keywords: rough volatility, VIX smile, Monte Carlo, Volterra process

JEL Classification: 60G15, 60G22, 91G20, 91G60, 91B25

Suggested Citation

Horvath, Blanka and Jacquier, Antoine and Tankov, Peter, Volatility Options in Rough Volatility Models (February 5, 2018). Available at SSRN: https://ssrn.com/abstract=3118425 or http://dx.doi.org/10.2139/ssrn.3118425

Blanka Horvath

ETH Zurich - Department of Mathematics ( email )

R¨amistrasse 101
Z¨urich, 8092
Switzerland

Antoine Jacquier (Contact Author)

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

Peter Tankov

Ecole Polytechnique, Paris ( email )

route de Saclay
Palaiseau, 91128
France

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