Integrated volatility and round-off error

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 ${\alpha }_n$, 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.

Published in at http://dx.doi.org/10.3150/08-BEJ170 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

References in corpus (1)

• Are volatility estimators robust with respect to modeling assumptions?

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