Bernoulli

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

Integrated volatility and round-off error

Mathieu Rosenbaum

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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 $α_n$, 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.

Article information

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

Dates
First available in Project Euclid: 28 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.bj/1251463277

Digital Object Identifier
doi:10.3150/08-BEJ170

Mathematical Reviews number (MathSciNet)
MR2555195

Zentralblatt MATH identifier
1200.62132

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

Citation

Rosenbaum, Mathieu. Integrated volatility and round-off error. Bernoulli 15 (2009), no. 3, 687--720. doi:10.3150/08-BEJ170. https://projecteuclid.org/euclid.bj/1251463277


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