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Frequency domain estimation of integrated volatility for Ito processes in the presence of market-microstructure noise

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Frequency domain estimation of integrated volatility for Ito processes in the presence of market-microstructure noise. / Olhede, S. C.; Sykulski, A. M.; Pavliotis, G. A.
In: Multiscale Modeling and Simulation, Vol. 8, No. 2, 2009, p. 393-427.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Olhede SC, Sykulski AM, Pavliotis GA. Frequency domain estimation of integrated volatility for Ito processes in the presence of market-microstructure noise. Multiscale Modeling and Simulation. 2009;8(2):393-427. doi: 10.1137/090756363

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Olhede, S. C. ; Sykulski, A. M. ; Pavliotis, G. A. / Frequency domain estimation of integrated volatility for Ito processes in the presence of market-microstructure noise. In: Multiscale Modeling and Simulation. 2009 ; Vol. 8, No. 2. pp. 393-427.

Bibtex

@article{b2a110d3ac5f4dd6a47f7e8fd7e1d984,
title = "Frequency domain estimation of integrated volatility for Ito processes in the presence of market-microstructure noise",
abstract = "This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented frequency by frequency, and the concept of the multiscale ratio is introduced to quantify the bias in the realized integrated volatility due to the observation error. The multiscale ratio is estimated from a single sample path, and a frequency-by-frequency bias correction procedure is proposed, which simultaneously reduces variance. We extend the method to include correlated observation errors and provide the implied time-domain form of the estimation procedure. The new method is implemented to estimate the integrated volatility for the Heston and other models, and the improved performance of our method over existing methods is illustrated by simulation studies.",
keywords = "bias correction, market microstructure noise, realized volatility, multiscale inference, Whittle likelihood, STOCHASTIC VOLATILITY, DIFFUSION-COEFFICIENT, TIME-SERIES, MODELS",
author = "Olhede, {S. C.} and Sykulski, {A. M.} and Pavliotis, {G. A.}",
year = "2009",
doi = "10.1137/090756363",
language = "English",
volume = "8",
pages = "393--427",
journal = "Multiscale Modeling and Simulation",
issn = "1540-3459",
publisher = "SIAM PUBLICATIONS",
number = "2",

}

RIS

TY - JOUR

T1 - Frequency domain estimation of integrated volatility for Ito processes in the presence of market-microstructure noise

AU - Olhede, S. C.

AU - Sykulski, A. M.

AU - Pavliotis, G. A.

PY - 2009

Y1 - 2009

N2 - This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented frequency by frequency, and the concept of the multiscale ratio is introduced to quantify the bias in the realized integrated volatility due to the observation error. The multiscale ratio is estimated from a single sample path, and a frequency-by-frequency bias correction procedure is proposed, which simultaneously reduces variance. We extend the method to include correlated observation errors and provide the implied time-domain form of the estimation procedure. The new method is implemented to estimate the integrated volatility for the Heston and other models, and the improved performance of our method over existing methods is illustrated by simulation studies.

AB - This paper proposes a novel multiscale estimator for the integrated volatility of an Ito process in the presence of market microstructure noise (observation error). The multiscale structure of the observed process is represented frequency by frequency, and the concept of the multiscale ratio is introduced to quantify the bias in the realized integrated volatility due to the observation error. The multiscale ratio is estimated from a single sample path, and a frequency-by-frequency bias correction procedure is proposed, which simultaneously reduces variance. We extend the method to include correlated observation errors and provide the implied time-domain form of the estimation procedure. The new method is implemented to estimate the integrated volatility for the Heston and other models, and the improved performance of our method over existing methods is illustrated by simulation studies.

KW - bias correction

KW - market microstructure noise

KW - realized volatility

KW - multiscale inference

KW - Whittle likelihood

KW - STOCHASTIC VOLATILITY

KW - DIFFUSION-COEFFICIENT

KW - TIME-SERIES

KW - MODELS

U2 - 10.1137/090756363

DO - 10.1137/090756363

M3 - Journal article

VL - 8

SP - 393

EP - 427

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

SN - 1540-3459

IS - 2

ER -