The COVID-19 pandemic had profound impacts on the global economy, initially triggering a severe economic downturn due to widespread lockdowns, this outbreak generated various economic shocks, a major one being the oil price crash. A brief understanding of how this pandemic is affecting the financial markets, empirical analysis is done on three financial markets. Three stock exchange markets are selected from emerging markets in South Asia (Pakistan, China, and India). The world crude oil market is selected as a reference, to how it transmits volatility to South Asian markets during the COVID-19 period. We employ a bivariate BEKK-GARCH model for analyzing the volatility spillover from November 19, 2019, to March 31, 2021. All markets show negative coefficients with the oil market, indicating that the previous day’s shocks in oil prices reduce today's stock market volatility, with significant values for India and Pakistan. China has a negative coefficient while the rest of the two markets show a positive and significant coefficient means past volatilities in the stock market decrease today’s oil market volatility, likely indicating a reactive or adaptive market behavior to stock volatility. Generally, oil price changes have a significant impact on these markets, with both immediate effects (via ARCH terms) and persistent effects (via GARCH terms). The study's findings offer valuable insights for policymakers, as they help identify the direction of spillovers among interconnected economies. Additionally, portfolio investors can use this information to effectively allocate weights to different asset classes when making investment decisions.