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This paper introduces novel volatility diffusion models to account for thestylized facts of high-frequency financial data such as volatility clustering,intra-day U-shape, and leverage effect. For example, the daily integratedvolatility of the proposed volatility process has a realized GARCH structurewith an asymmetric effect on log-returns. To further explain theheavy-tailedness of the financial data, we assume that the log-returns have afinite $2b$-th moment for $b \in (1,2]$. Then, we propose a Huber regressionestimator which has an optimal convergence rate of $n^{(1-b)/b}$. We alsodiscuss how to adjust bias coming from Huber loss and show its asymptoticproperties.

Volatility Models for Stylized Facts of High-Frequency Financial Data