# Forecasting security's volatility using low-frequency historical data, high-frequency historical data and option-implied volatility

## TL;DR

This paper introduces two new econometric models that combine low-frequency, high-frequency, and option-implied data to improve security volatility forecasting, demonstrating superior performance over existing models.

## Contribution

The paper develops two novel models integrating multiple data sources for volatility forecasting and provides their theoretical properties and empirical validation.

## Key findings

- Models outperform existing methods with 5-minute high-frequency data
- GARCH-Itô-OI model incorporates option-implied volatility directly
- GARCH-Itô-IV model extracts useful info without direct influence

## Abstract

Low-frequency historical data, high-frequency historical data and option data are three major sources, which can be used to forecast the underlying security's volatility. In this paper, we propose two econometric models, which integrate three information sources. In GARCH-It\^{o}-OI model, we assume that the option-implied volatility can influence the security's future volatility, and the option-implied volatility is treated as an observable exogenous variable. In GARCH-It\^{o}-IV model, we assume that the option-implied volatility can not influence the security's volatility directly, and the relationship between the option-implied volatility and the security's volatility is constructed to extract useful information of the underlying security. After providing the quasi-maximum likelihood estimators for the parameters and establishing their asymptotic properties, we also conduct a series of simulation analysis and empirical analysis to compare the proposed models with other popular models in the literature. We find that when the sampling interval of the high-frequency data is 5 minutes, the GARCH-It\^{o}-OI model and GARCH-It\^{o}-IV model has better forecasting performance than other models.