Volatility models for stylized facts of high-frequency financial data

This article introduces novel volatility diffusion models to account for the stylized facts of high-frequency financial data such as volatility clustering, intraday 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 that 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.