The Estimation of the Spot Volatility for Diffusion Process

In this paper, we propose a Gasser-Muller type spot volatility estimator (abbreviated as GM type estimator) for diffusion process, which is weighted by integrals, it is different from the kernel spot volatility estimator discussed by Kristensen (2010). Under more general conditions, the asymptotic unbiasedness and the asymptotic normality of the GM type estimator are derived. The simulation results show that the GM type spot volatility estimator has good estimation effect, and its mean square error tends to be less than that of the kernel spot volatility estimator discussed by Kristensen (2010), so it provides a selection method for estimating the spot volatility in high frequency data environment.