Modeling S&P500 returns with GARCH models

Rodrigo Alfaro, Alejandra Inzunza

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.

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Year of publication:	2023
Authors:	Alfaro, Rodrigo ; Inzunza, Alejandra
Published in:	Latin American journal of central banking : LAJCB. - Amsterdam : Elsevier, ISSN 2666-1438, ZDB-ID 3035191-1. - Vol. 4.2023, 3, Art.-No. 100096, p. 1-11
Subject:	GARCH option pricing models \| Tail-risk statistics \| VIX \| ARCH-Modell \| ARCH model \| Optionspreistheorie \| Option pricing theory \| Schätzung \| Estimation \| Kapitalmarktrendite \| Capital market returns \| Volatilität \| Volatility