Modelling the Volatility Dynamics of WTI Crude Oil and the US Dollar Index Using GARCH(1,1) Model

Abstract

 The period from 2020 to 2026 was characterized by significant economic and geopolitical events, making it a crucial period to analyze the volatility dynamics across asset classes. Crude oil and currency market volatility have been extensively analyzed in isolation but there are only few empirical studies that have compared both markets in a joint GARCH framework. The study focuses on the volatility of West Texas Intermediate (WTI) crude oil and the US Dollar Index (USDX) of daily closing prices from January 2, 2020 to June 30, 2026. Models were estimated using quasi-maximum likelihood estimation with robust standard errors, following Augmented Dickey–Fuller (ADF) and ARCH-LM tests, which pointed to GARCH(1,1) models. The results show that the volatilities are different. WTI has a high ARCH coefficient () and a near-integrated volatility persistence (), and a robust standard error of 0.2415, which suggest very persistent volatility shocks. By contrast, the USDX exhibits a low ARCH coefficient (), a high GARCH coefficient () and a volatility half-life of about 20 trading days. The results offer evidence for the different persistence of volatility in commodity and currency markets, which have implications on volatility forecasting, portfolio allocation and financial risk management.