The purpose of this paper is to examine whether the volatility of the West Texas Intermediate oil spot returns (WTIR) is affected by the Texas Light Sweet oil futures returns (FUR), the exchange rate returns between the US dollar and the Euro (ERR), and the S&P 500 energy index returns (EIR), and if any of those have changed over time. The daily data of the WTIR, the FUR, the ERR, and the EIR between the period of January 4, 2000 and September 30, 2009, were utilized. The empirical results of the multivariate GARCH of the BEKK model indicated that the WTIR is significantly affected by its own past volatility, and by the volatility of FUR, ERR, and EIR. Most likely, WTIR employs a structural conversion in our dummy variable for selected time points. This suggests that investors could use the FUR’s past volatility as a basis for WTIR purchase. In addition, the changes in ERR’s and EIR’s past volatility can be partially used as a basis for the same purpose.