This paper aims to model the volatility of returns for selected stock indices and examine the causal relationships between the markets using the historical daily prices of the Financial Times Stock Exchange (FTSE), Bursa Malaysia Kuala Lumpur Composite Index (KLCI), the Indonesia Stock Exchange Index (LQ45), and the Stock Exchange of Thailand (SET) from January 2008 to November 2019. The study employs univariate GARCH models that are prominent in capturing the volatility clustering of financial instruments in association with the Box–Jenkins methodology for better estimation. Generally, the ARMA-GARCH model is used to capture the volatility series, while the Granger causality test examines the causal directions between the markets. The findings revealed leverage effects on the markets, with the outperformance of the EGARCH in analyzing the empirical properties of stock returns. An initial test that yielded positive correlations suggests the existence of co-movement between the derived volatility series. The study concluded bidirectional causal relationships between the selected markets, and based on the resulting relationships, it is proposed that supervision of markets among the ASEAN members could be advantageous in predicting the corresponding market performance.