This study investigates the need for variants of GARCH model when the former fails to fully embrace clumping volatility of either a positive or negative shock via asymmetrical effect, long-memory, high-frequency, and leverage effect. The volatility effect of distributions of crude oil (prices, barrels produced and exported) in Nigeria, for the period of fifteen (15) (1: 2006 to 8:2020) years obtained from Nigeria National Petroleum Corporation (NNPC) bulletin were examined via GARCH and it variants. Exploratory Data Analysis (EDA) and time plot analyzes were carried-out on the one hundred and seventy-six (176) data points. It was deduced that GARCH (2,1) optimally generalized the prices of crude oil among its variants of gjrGARCH (2,1), apARCH (2,1), iGARCH (2,1), and csGARCH (2,1), and that positive and negative shocks did not have the same impact on the volatility of prices of crude oil. In a similar vein, iGARCH (1,1) optimized barrels of crude oil produced and exported among eGARCH (1,1), GARCCH (1,1), gjrGARCH (1,1), apARCH (1,1), iGARCH (1,1), and csGARCH (1,1) for the years of studied. However, it was inferred that positive shock as real meaningful impact on the clumping volatility on barrels of crude oil produced and exported while negative shock as no meaningful impact on the volatility on barrels of crude oil produced and exported.