Modeling S&P500 returns with GARCH models

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