Integrated volatility and round-off error
Mathieu Rosenbaum
Source: Bernoulli Volume 15, Number 3
(2009), 687-720.
Abstract
We consider a microstructure model for a financial asset, allowing for price discreteness and for a diffusive behavior at large sampling scale. This model, introduced by Delattre and Jacod, consists in the observation at the high frequency n, with round-off error αn, of a diffusion on a finite interval. We give from this sample estimators for different forms of the integrated volatility of the asset. Our method is based on variational properties of the process associated with wavelet techniques. We prove that the accuracy of our estimation procedures is αn∨n−1/2. Using compensated estimators, limit theorems are obtained.
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Keywords: diffusion models; high frequency data; integrated volatility; microstructure noise; round-off error; variation methods; wavelets
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Permanent link to this document: http://projecteuclid.org/euclid.bj/1251463277
Digital Object Identifier: doi:10.3150/08-BEJ170
Mathematical Reviews number (MathSciNet): MR2555195
Zentralblatt MATH identifier: 05815951
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