Description

This paper provides several estimates of the parameters of GARCH models for the S&P500 index, based on returns and CBOE VIX. Using a daily sample from 2007 to 2022, we conclude that adding the information of VIX improves the estimates of the long-term volatility. We provide an external validation of the model using an option-based index reported by the Federal Reserve of Minneapolis, allowing us to propose a calibrate model for tracking the tail-risk of this stock index.