Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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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 -