NOISY HIGH FREQUENCY DATA-BASED ESTIMATION OF VOLATILITY FUNCTION WITH APPLICATIONS

Abstract

Diffusion models have been widely used to describe the stochastic dynamics of the underlying economic variables. Renò ( 2008 ) introduced a nonparametric estimator of the volatility function, which is based on the estimation of quadratic variation between observations by means of realized variance. However, they may be misleading when one uses intraday data to implement directly the estimator, because intraday data display microstructure effects that could seriously distort the estimation. To filter out the impact of microstructure noise on the estimation of the volatility function, in this paper we propose an improved estimator when there is microstructure noise in the observed price. Also, we show that the proposed estimator has the same asymptotic properties as the Renò estimator when the step of discretization inclines to zero. Some simulations and empirical applications on Shanghai Stock Exchange data from March 3, 2002 to December 31, 2008 are used to illustrate the finite sample performance of the proposed estimator.