STOCK MARKET VOLATILITY MODELING WITH MACRO-FINANCIAL FACTORS: THE AR-X-GARCH APPROACH

Abstract

The purpose of this study is to examine the dynamics of S&P 500 index volatility using daily data from January 1, 2020, to November 1, 2025. The analysis focuses on volatility persistence, clustering behavior, and the effects of the EUR/USD exchange rate and WTI crude oil prices on the stock market. For this purpose, daily return series for the S&P 500 index, the EUR/USD exchange rate, and WTI crude oil prices are employed. The stationarity properties of the series are examined using unit root tests, and the presence of conditional heteroskedasticity is confirmed prior to the estimation process. Volatility dynamics are modeled using the GARCH(1,1) framework, while cross-market interactions are analyzed through an AR-X-GARCH specification. Risk performance is further assessed through Value-at-Risk (VaR) backtesting at the 99% confidence level. The empirical findings indicate that all return series are stationary and exhibit significant volatility clustering. The GARCH(1,1) estimates reveal strong volatility persistence, confirming that market risk evolves over time. The AR-X-GARCH results show that EUR/USD exchange rate returns have a negative and statistically significant effect on S&P 500 returns, while WTI crude oil returns exert a positive and economically meaningful impact. VaR backtesting results support the reliability of the risk estimates. Overall, the findings demonstrate that foreign exchange and commodity markets play a decisive role in shaping stock market volatility and that GARCH-type models can be effectively employed in portfolio risk measurement and financial stability analysis.