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