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@article{Bennedsen:2017:10.1007/s00780-017-0335-5,
author = {Bennedsen, M and Lunde, A and Pakkanen, MS},
doi = {10.1007/s00780-017-0335-5},
journal = {Finance and Stochastics},
pages = {931--965},
title = {Hybrid scheme for Brownian semistationary processes},
url = {http://dx.doi.org/10.1007/s00780-017-0335-5},
volume = {21},
year = {2017}
}

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TY  - JOUR
AB  - We introduce a simulation scheme for Brownian semistationary processes, whichis based on discretizing the stochastic integral representation of the processin the time domain. We assume that the kernel function of the process isregularly varying at zero. The novel feature of the scheme is to approximatethe kernel function by a power function near zero and by a step functionelsewhere. The resulting approximation of the process is a combination ofWiener integrals of the power function and a Riemann sum, which is why we callthis method a hybrid scheme. Our main theoretical result describes theasymptotics of the mean square error of the hybrid scheme and we observe thatthe scheme leads to a substantial improvement of accuracy compared to theordinary forward Riemann-sum scheme, while having the same computationalcomplexity. We exemplify the use of the hybrid scheme by two numericalexperiments, where we examine the finite-sample properties of an estimator ofthe roughness parameter of a Brownian semistationary process and study MonteCarlo option pricing in the rough Bergomi model of Bayer et al. (2015),respectively.
AU  - Bennedsen,M
AU  - Lunde,A
AU  - Pakkanen,MS
DO  - 10.1007/s00780-017-0335-5
EP  - 965
PY  - 2017///
SN  - 0949-2984
SP  - 931
TI  - Hybrid scheme for Brownian semistationary processes
T2  - Finance and Stochastics
UR  - http://dx.doi.org/10.1007/s00780-017-0335-5
UR  - http://hdl.handle.net/10044/1/46133
VL  - 21
ER  -

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