Hybrid scheme for Brownian semistationary processes
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Accepted version
Published version
Author(s)
Bennedsen, M
Lunde, A
Pakkanen, MS
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.
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.
Date Issued
2017-10-01
Date Acceptance
2017-05-02
Citation
Finance and Stochastics, 2017, 21 (4), pp.931-965
ISSN
0949-2984
Publisher
Springer
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.
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.
License URL
Subjects
math.PR
math.PR
q-fin.PR
60G12, 60G22, 65C20, 91G60, 62M09
Notes
32 pages, 4 figures, v3: the proof of Proposition 2.1 amended plus some other minor improvements
Publication Status
Published
Date Publish Online
2017-06-28