• Bernoulli
  • Volume 15, Number 3 (2009), 687-720.

Integrated volatility and round-off error

Mathieu Rosenbaum

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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 $α_n$, 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 $α_n∨n^{−1/2}$. Using compensated estimators, limit theorems are obtained.

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Bernoulli, Volume 15, Number 3 (2009), 687-720.

First available in Project Euclid: 28 August 2009

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diffusion models high frequency data integrated volatility microstructure noise round-off error variation methods wavelets


Rosenbaum, Mathieu. Integrated volatility and round-off error. Bernoulli 15 (2009), no. 3, 687--720. doi:10.3150/08-BEJ170.

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