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The volatility is a measure for the uncertainty of an asset's return and is used to reflect the risk level of a financial asset. In this article, we consider the double kernel nonparametric estimator for the volatility function in a diffusion model over a finite-time span based on high frequency sampling data. Under the minimum conditions, the asymptotic mixed normality for the underlying estimator is derived. Moreover, the better finite-sample performance as variance reduction and even mean squared error reduction of the proposed estimator is verified through a Monte Carlo simulation study and an empirical analysis on overnight Shibor in China. [ABSTRACT FROM AUTHOR]

In this article, we consider non parametric range-based estimation procedure for diffusion processes and propose a instantaneous volatility estimator. Under some weak conditions, we certify that the proposed estimator has convergence in probability. Adding some necessary conditions, we prove a central limit theorem. By inference, we reach a conclusion that, with high frequency data in hand, the proposed estimator is more precise than those pure realized instantaneous volatility ones. Numerical simulation illustrates the finite sample properties of the proposed estimator. [ABSTRACT FROM AUTHOR]

In this paper, we estimate the integrated volatility of Itô semimartingale when sampling times are endogenous. The estimator is proved to be consistent, and is robust to jumps, regardless of whether they are finite and infinite activity jumps. We also establish a central limit theorem for the estimator in a general endogenous time setting when the jumps have finite variation. Simulation is also included to illustrate the performance of the proposed procedure. [ABSTRACT FROM PUBLISHER]