# Volatility Analysis with Realized GARCH-Ito Models

## TL;DR

This paper develops a unified realized GARCH-Ito model for high-frequency financial data, capturing both continuous and jump components, and proposes estimation methods validated through simulations and empirical analysis.

## Contribution

It introduces the realized GARCH-Ito model embedding discrete realized GARCH in continuous volatility, with new estimation techniques and empirical validation.

## Key findings

- Model effectively captures volatility dynamics with jumps.
- Proposed estimation methods show good finite sample performance.
- Empirical application demonstrates practical usefulness.

## Abstract

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.