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Hybrid scheme for Brownian semistationary processes

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Hybrid scheme for Brownian semistationary processes. / Bennedsen, Mikkel; Lunde, Asger; Pakkanen, Mikko S.

In: Finance and Stochastics, Vol. 21, No. 4, 10.2017, p. 931-965.

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@article{5220617b43f94ed2b394724c77f2a663,
title = "Hybrid scheme for Brownian semistationary processes",
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. (Quant. Finance 16:887-904, 2016), respectively.",
keywords = "Stochastic simulation, Discretization, Brownian semistationary process, Stochastic volatility, Regular variation, Estimation, Option pricing, Rough volatility, Volatility smile, SPOT PRICES, VOLATILITY, TURBULENCE, MODELS",
author = "Mikkel Bennedsen and Asger Lunde and Pakkanen, {Mikko S.}",
year = "2017",
month = oct,
doi = "10.1007/s00780-017-0335-5",
language = "English",
volume = "21",
pages = "931--965",
journal = "Finance and Stochastics",
issn = "0949-2984",
publisher = "Springer",
number = "4",

}

RIS

TY - JOUR

T1 - Hybrid scheme for Brownian semistationary processes

AU - Bennedsen, Mikkel

AU - Lunde, Asger

AU - Pakkanen, Mikko S.

PY - 2017/10

Y1 - 2017/10

N2 - 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. (Quant. Finance 16:887-904, 2016), respectively.

AB - 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. (Quant. Finance 16:887-904, 2016), respectively.

KW - Stochastic simulation

KW - Discretization

KW - Brownian semistationary process

KW - Stochastic volatility

KW - Regular variation

KW - Estimation

KW - Option pricing

KW - Rough volatility

KW - Volatility smile

KW - SPOT PRICES

KW - VOLATILITY

KW - TURBULENCE

KW - MODELS

U2 - 10.1007/s00780-017-0335-5

DO - 10.1007/s00780-017-0335-5

M3 - Journal article

VL - 21

SP - 931

EP - 965

JO - Finance and Stochastics

JF - Finance and Stochastics

SN - 0949-2984

IS - 4

ER -