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The Estimation of the Spot Volatility for Diffusion Process

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Document pages: 16 pages

Abstract: In thispaper, we propose a Gasser-Müller type spot volatility estimator (abbreviatedas GM type estimator) for diffusion process, which is weighted by integrals, itis different from the kernel spot volatility estimator discussed by Kristensen(2010). Under more general conditions, the asymptotic unbiasedness and theasymptotic normality of the GM type estimator are derived. The simulationresults show that the GM type spot volatility estimator has good estimationeffect, and its mean square error tends to be less than that of the kernel spotvolatility estimator discussed by Kristensen (2010), so it provides a selectionmethod for estimating the spot volatility in high frequency data environment.

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