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Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach

25 Pages Posted: 21 Nov 2004  

Lan Zhang

University of Illinois at Chicago - Department of Finance

Date Written: December 29, 2005

Abstract

With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed asset returns contain error or noise, for example, in the form of microstructure noise. The former (consistency) has been addressed heavily in the recent literature, however, the resulting estimator is not quite efficient. In Zhang, Mykland, Ait-Sahalia (2003), the best estimator converges to the true volatility only at the rate of n wedge{-1/6}. In this paper, we propose an estimator, the Multi-scale Realized Volatility (MSRV), which converges to the true volatility at the rate of n wedge{-1/4}, which is the best attainable. We have shown a central limit theorem for the MSRV estimator, which permits setting intervals for the true integrated volatility on the basis of MSRV.

Keywords: Consistency, dependent noise, discrete observation, Ito process, microstructure noise, observation error, rate of convergence, realized volatility

JEL Classification: C13, C14, C22, G10

Suggested Citation

Zhang, Lan, Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach (December 29, 2005). Available at SSRN: https://ssrn.com/abstract=619682 or http://dx.doi.org/10.2139/ssrn.619682

Lan Zhang (Contact Author)

University of Illinois at Chicago - Department of Finance ( email )

601 South Morgan Street
Chicago, IL 60607
United States

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