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Hybrid scheme for Brownian semistationary processes

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Bennedsen-Lunde-Pakkanen-2017-revised.pdfAccepted version481.78 kBAdobe PDFView/Open
10.1007%2Fs00780-017-0335-5.pdfPublished version1.06 MBAdobe PDFView/Open
Title: Hybrid scheme for Brownian semistationary processes
Authors: Bennedsen, M
Lunde, A
Pakkanen, MS
Item Type: Journal Article
Abstract: We introduce a simulation scheme for Brownian semistationary processes, which is based on discretizing the stochastic integral representation of the process in the time domain. We assume that the kernel function of the process is regularly varying at zero. The novel feature of the scheme is to approximate the kernel function by a power function near zero and by a step function elsewhere. The resulting approximation of the process is a combination of Wiener integrals of the power function and a Riemann sum, which is why we call this method a hybrid scheme. Our main theoretical result describes the asymptotics of the mean square error of the hybrid scheme and we observe that the scheme leads to a substantial improvement of accuracy compared to the ordinary forward Riemann-sum scheme, while having the same computational complexity. We exemplify the use of the hybrid scheme by two numerical experiments, where we examine the finite-sample properties of an estimator of the roughness parameter of a Brownian semistationary process and study Monte Carlo option pricing in the rough Bergomi model of Bayer et al. (2015), respectively.
Issue Date: 28-Jun-2017
Date of Acceptance: 2-May-2017
URI: http://hdl.handle.net/10044/1/46133
DOI: https://dx.doi.org/10.1007/s00780-017-0335-5
ISSN: 1432-1122
Publisher: Springer Verlag (Germany)
Start Page: 931
End Page: 965
Journal / Book Title: Finance and Stochastics
Volume: 21
Issue: 4
Copyright Statement: © The Author(s) 2017 This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Keywords: math.PR
q-fin.PR
60G12, 60G22, 65C20, 91G60, 62M09
0102 Applied Mathematics
0104 Statistics
Finance
Notes: 32 pages, 4 figures, v3: the proof of Proposition 2.1 amended plus some other minor improvements
Publication Status: Published
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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