Abstract
In this paper, we propose a Gasser-Müller 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.
Highlights
Volatility is the main component of describing the price movement towards financial market, so we need to use the observed actual data to estimate volatility
We propose a Gasser-Müller type spot volatility estimator for diffusion process, which is weighted by integrals, it is different from the kernel spot volatility estimator discussed by Kristensen (2010)
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
Summary
Volatility is the main component of describing the price movement towards financial market, so we need to use the observed actual data to estimate volatility. By using the properties of Brown’s motion path, when the price obeys the jump-diffusion model with finite jump, another estimator of integrated volatility, the realized threshold volatility, is proposed, and the central limit theorem is obtain by Mancini [15] [16] (2004, 2009). Wang [25] (2008) employs a bivariate diffusion to model the price and volatility of an asset and investigates kernel type estimators of spot volatility based on high-frequency return data. They establish both pointwise and global asymptotic distributions for the estimators.
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