Functional central limit theorems for rough volatility

Horvath, Blanka, Jacquier, Antoine, Muguruza, Aitor and Søjmark, Andreas ORCID: 0000-0001-7488-0221 (2024) Functional central limit theorems for rough volatility. Finance and Stochastics, 28 (3). 615 - 661. ISSN 0949-2984

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Abstract

The non-Markovian nature of rough volatility makes Monte Carlo methods challenging, and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra processes, based on an extension of Donsker’s approximation of Brownian motion to the fractional Brownian case with arbitrary Hurst exponent H∈(0,1). Some of the most relevant consequences of this ‘rough Donsker (rDonsker) theorem’ are functional weak convergence results in Skorokhod space for discrete approximations of a large class of rough stochastic volatility 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). Our rDonsker theorem further provides a weak convergence proof for the hybrid scheme itself and allows constructing binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan options.

Item Type:	Article
Official URL:	https://link.springer.com/journal/780
Additional Information:	© 2024 The Author(s)
Divisions:	Statistics
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
JEL classification:	G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice; Investment Decisions
Date Deposited:	29 Apr 2024 14:36
Last Modified:	15 Nov 2024 07:42
URI:	http://eprints.lse.ac.uk/id/eprint/122848

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