Contemporary empirical literature is rich in studies that have modelled and forecasted the nature and behavior of volatility of equity returns in both emerging and advanced stock markets. Modelling and estimating volatility is crucial in dynamic risk management, equity valuation and portfolio diversification. However, South African financial markets have not received ample attention in this regard. It is against this backdrop that we sought to determine the nature and behavior of volatility inherent in the South African stock market. Furthermore, we examined the effect of the 2014 global oil crisis on the volatility spillover in this market. The FTSE/JSE Top 40 index of the Johannesburg Stock Exchange has been selected as the study sample. Sample data for the period spans from October 14, 2009 to December 31, 2019, wherein the crisis period is from March 03, 2014 to February 27, 2015. Conditional volatility has been modelled and estimated using GARCH (1.1), GARCH-M (1.1), TGARCH (1.1) and EGARCH (1.1). The log likelihood, Akaike Information Criterion and Bayesian Information Criterion have been followed for model selection. The results showed that the EGARCH model is the most suitable for predicting the behavior of equity returns including for the global oil crisis period. JEL Classification Codes: C01, C13, C52, C53, C87.