2019/07/02 by Xinyu Song, Donggyu Kim, Song, Xinyu +10
Economics, Econometrics and Finance · #Applications (stat.AP) #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Methodology (stat.ME) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1907.01175
openalex publication_date 2019/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the discrete realized GARCH structure in the continuous instantaneous volatility process. The key feature of the proposed model is that the corresponding conditional daily integrated volatility adopts an autoregressive structure where both integrated volatility and jump variation serve as innovations. We name it as the realized GARCH-Ito model. Given the autoregressive structure in the conditional daily integrated volatility, we propose a quasi-likelihood function for parameter estimation and establish its asymptotic properties. To improve the parameter estimation, we propose a joint quasi-likelihood function that is built on the marriage of daily integrated volatility estimated by high-frequency data and nonparametric volatility estimator obtained from option data. We conduct a simulation study to check the finite sample performance of the proposed methodologies and an empirical study with the S&P500 stock index and option data.