Functional Central Limit Theorems for Rough Volatility

30 Pages Posted: 30 Nov 2017 Last revised: 10 May 2019

See all articles by Blanka Horvath

Blanka Horvath

ETH Zürich - Department of Mathematics

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Aitor Muguruza

Imperial College London; Kaiju Capital Management

Date Written: November 28, 2017

Abstract

We extend Donsker’s approximation of Brownian motion to fractional Brownian motion with Hurst exponent H∈(0,1) and to Volterra-like processes. Some of the most relevant consequences of our ‘rough Donsker (rDonsker) Theorem’ are convergence results for discrete approximations of a large class of rough models. This justifies the validity of simple and easy-to-implement Monte-Carlo methods, for which we provide detailed numerical recipes. We test these against the current benchmark Hybrid scheme and find remarkable agreement (for a large range of values of H). This rDonsker Theorem further provides a weak convergence proof for the Hybrid scheme itself, and allows to construct binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan.

Keywords: functional limit theorems, Gaussian processes, invariance principles, fractional Brownian motion, rough volatility, binomial trees

JEL Classification: G20, G99, G60, B25

Suggested Citation

Horvath, Blanka and Jacquier, Antoine and Muguruza, Aitor, Functional Central Limit Theorems for Rough Volatility (November 28, 2017). Available at SSRN: https://ssrn.com/abstract=3078743 or http://dx.doi.org/10.2139/ssrn.3078743

Blanka Horvath

ETH Zürich - Department of Mathematics ( email )

R¨amistrasse 101
Raemistr. 101
Z¨urich, 8092
Switzerland

Antoine Jacquier

Imperial College London ( email )

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

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

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Aitor Muguruza (Contact Author)

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Kaiju Capital Management ( email )

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