**Abstract**

This present study examines the volatility effects of the oil price on the stock price returns in Nigeria from the period of 2000M(12) to 2020M(4) on a monthly data using both standard GARCH and non-linear GARCH models. The motivation for the present study is the recent fall in the global oil price of Brent Crude to US\$15.25 per barrel due to the outbreak of the Corona Virus (COVID-19). Consequentially, the Nigerian stock market (NSE) responded with a fall of 4172 point or by a fall of 15.53%. After establishing the presence of heteroscedasticity through the ARCH test and volatility clustering through the returns, the outcome of the study contributes to knowledge by providing financial information and signals to investors about the best GARCH model response to proactively and successfully use to model global oil price shocks so as to reduce financial risk in Nigeria's stock market.

**Keywords:** oil price volatility, stock market returns, linear and non-linear GARCH models, Nigeria
