Research on the Volatility of the S&P 500 Stock Index Based on GARCH Family Models

Abstract

Volatility is an important issue in financial research. In this paper, in order to study the volatility of the S&P 500 index, which is representative of the American stock market, is used as research object, and the daily closing prices from July 2018 to July 2022 are selected. It has since become widely accepted in the academic community that stock return volatility is slow moving. Therefore, the series cannot accurately capture the characteristics of volatility. Developing the GARCH model gives us an effective way of describing return volatility. The statistical software EViews is initially utilized to take the logarithmic difference of the data and obtain the daily return series of the past five years, and to test if the time series has ARCH effect. The results suggest that the returns in the series are not correlated with each other, and that volatility has an obvious correlation, which makes it suitable to model with a GARCH family model.