Integrated volatility and round-off error

Details Integrated volatility and round-off error Integrated volatility and round-off error

2009-09-04

arxiv.org/abs/0909.0835v1

Bernoulli 2009, Vol. 15, No. 3, 687-720

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ170 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ170

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 $\alpha_n$, 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 $\alpha_n\vee n^{-1/2}$. Using compensated estimators, limit theorems are obtained.

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