Volatility analysis with realized GARCH-Itô models

This paper introduces a unified approach for modeling high-frequency financial data that can accommodate both the continuous-time jump–diffusion and discrete-time realized GARCH model by embedding discrete structure in continuous instantaneous volatility process. The key feature of proposed is corresponding conditional daily integrated adopts an autoregressive structure, where jump variation serve as innovations. We name it GARCH-Itô model. Given volatility, we propose quasi-likelihood function parameter estimation establish its asymptotic properties. To improve estimation, joint built on marriage estimated nonparametric estimator obtained from option data. conduct simulation study to check finite sample performance methodologies empirical with S&P500 stock index