Microstructure Noise, Integrated Volatility, and Rounding Error

• Activity Number: 79
• Type: Invited
• Date/Time: Monday, August 4, 2008 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economics Statistics Section
• Author(s): Mathieu Rosenbaum*+
• Companies: University Paris-Est and CREST-ENSAE
• Keywords: Microstructure noise ; Diffusion models ; Integrated volatility ; High frequency data ; Round-off error ; Variation methods.

Abstract

We consider a microstructure model for a financial asset, allowing for prices discreteness and for a diffusive behavior at large sampling scale. This model consists in the observation at the high frequency n, with rounding error a(n), of a diffusion on a finite time interval. From this sample, we give estimators of the absolute and relative integrated volatilities of the asset. Our method is based on the use of variational properties of the process in a wavelet setting. We prove the accuracy of our estimation procedures is max(a(n), n^{-1/2}). Using compensated estimators, limit theorems are given in the case of a homogeneous diffusion coefficient.