Functional central limit theorems for rough volatility

Blanka Horvath, Antoine Jacquier, Aitor Muguruza and Andreas Søjmark

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: binomial trees; fractional brownian motion; functional limit theorems; rough volatility; Early Postdoc.Mobility grant 165248; Imperial CDT in Financial Computing & Analytics; T032146 grant (search for similar items in EconPapers)
JEL-codes: G11 (search for similar items in EconPapers)
Pages: 47 pages
Date: 2024-07-01
New Economics Papers: this item is included in nep-rmg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in Finance and Stochastics, 1, July, 2024, 28(3), pp. 615 - 661. ISSN: 0949-2984

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