Exponential GARCH-Ito Volatility Models

This paper introduces a novel Ito diffusion process to model high-frequency financial data, which can accommodate low-frequency volatility dynamics by embedding the discrete-time non-linear exponential GARCH structure with log-integrated in continuous instantaneous process. The key feature of proposed is that, unlike existing GARCH-Ito models, has structure, ensures that volatilities have realized structure. We call this (ERGI) model. Given auto-regressive volatility, we propose quasi-likelihood estimation procedure for parameter and establish its asymptotic properties. conduct simulation study check finite sample performance an empirical 50 assets among S\&P 500 compositions. numerical studies show advantages new