This paper investigates the nature of volatility characteristics of stock returns in the Bangladesh stock markets employing daily all share price index return data of Dhaka Stock Exchange (DSE) and Chittagong Stock Exchange (CSE) from 02 January 1993 to 27 January 2013 and 01 January 2004 to 20 August 2015 respectively. Furthermore, the study explores the adequate volatility model for the stock markets in Bangladesh. Results of the estimated MA(1)-GARCH(1,1) model for DSE and GARCH(1,1) model for CSE reveal that the stock markets of Bangladesh capture volatility clustering, while volatility is moderately persistent in DSE and highly persistent in CSE. Estimated MA(1)-EGARCH(1,1) model shows that effect of bad news on stock market volatility is greater than effect induced by good news in DSE, while EGARCH(1,1) model displays that volatility spill over mechanism is not asymmetric in CSE. Therefore, it is concluded that return series of DSE show evidence of three common events, namely volatility clustering, leptokurtosis and the leverage effect, while return series of CSE contains leptokurtosis, volatility clustering and long memory. Finally, this study explores that MA(1)-GARCH(1,1) is the best model for modeling volatility of Dhaka stock market returns, while GARCH models are inadequate for volatility modeling of CSE returns.