Functional quantization of rough volatility and applications to volatility derivatives
Author(s)
Bonesini, Ofelia
Callegaro, Giorgia
Jacquier, Antoine
Type
Journal Article
Abstract
We develop a product functional quantization of rough volatility. Since the optimal quantizers can be computed offline, this new technique, built on the insightful works by [Luschgy, H. and Pagès, G., Functional quantization of Gaussian processes. J. Funct. Anal., 2002, 196(2), 486–531; Luschgy, H. and Pagès, G., High-resolution product quantization for Gaussian processes under sup-norm distortion. Bernoulli, 2007, 13(3), 653–671; Pagès, G., Quadratic optimal functional quantization of stochastic processes and numerical applications. In Monte Carlo and Quasi-Monte Carlo Methods 2006, pp. 101–142, 2007 (Springer: Berlin Heidelberg)], becomes a strong competitor in the new arena of numerical tools for rough volatility. We concentrate our numerical analysis on the pricing of options on the VIX and realized variance in the rough Bergomi model [Bayer, C., Friz, P.K. and Gatheral, J., Pricing under rough volatility. Quant. Finance, 2016, 16(6), 887–904] and compare our results to other benchmarks recently suggested.
Date Issued
2023
Date Acceptance
2023-10-12
Citation
Quantitative Finance, 2023, 23 (12), pp.1769-1792
ISSN
1469-7688
Publisher
Taylor and Francis Group
Start Page
1769
End Page
1792
Journal / Book Title
Quantitative Finance
Volume
23
Issue
12
Copyright Statement
© 2023 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricteduse, distribution, and reproduction in any medium, provided the original work is properly cited. The terms on which this article has been published allow the posting of theAccepted Manuscript in a repository by the author(s) or with their consent.
License URL
Identifier
https://doi.org/10.1080/14697688.2023.2273414
Publication Status
Published
Date Publish Online
2023-12-03