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Frequency Domain Estimation of Integrated Volatility for Ito Processes in the Presence of Market-Microstructure Noise

Frequency Domain Estimation of Integrated Volatility for Ito Processes in the Presence of Market-Microstructure Noise
Frequency Domain Estimation of Integrated Volatility for Ito Processes in the Presence of Market-Microstructure Noise
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.
bias correction, market microstructure noise, realized volatility, multiscale inference, Whittle likelihood
393-427
Olhede, S.C.
b0f12dd2-270c-440e-8c01-86a2f36c390e
Sykulski, A.M.
687d5481-dc05-44c6-af21-2452c135394f
Pavliotis, G.A.
2041971d-67c4-4cb0-88c9-c7b2443f59d7
Olhede, S.C.
b0f12dd2-270c-440e-8c01-86a2f36c390e
Sykulski, A.M.
687d5481-dc05-44c6-af21-2452c135394f
Pavliotis, G.A.
2041971d-67c4-4cb0-88c9-c7b2443f59d7

Olhede, S.C., Sykulski, A.M. and Pavliotis, G.A. (2009) Frequency Domain Estimation of Integrated Volatility for Ito Processes in the Presence of Market-Microstructure Noise. SIAM - Multiscale Modeling and Simulation, 8 (2), 393-427.

Record type: Article

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.

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Published date: 9 December 2009
Keywords: bias correction, market microstructure noise, realized volatility, multiscale inference, Whittle likelihood
Organisations: Electronics & Computer Science

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Local EPrints ID: 268756
URI: https://eprints.soton.ac.uk/id/eprint/268756
PURE UUID: 9463c9d1-2765-4d7d-9897-b6efc501a9d8

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Date deposited: 18 Mar 2010 16:17
Last modified: 06 Aug 2019 18:57

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