Integrated volatility and round-off error

TL;DR

This paper develops estimators for integrated volatility in a high-frequency financial model accounting for price discreteness and round-off errors, using wavelet techniques and proving their accuracy and limit behavior.

Contribution

It introduces a novel estimation method for integrated volatility that incorporates round-off errors and demonstrates its theoretical properties.

Findings

Estimation accuracy is characterized by _n  n^{-1/2}.

Limit theorems for the proposed estimators are established.

Wavelet-based techniques effectively handle price discreteness and noise.

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.