This study investigates volatility pattern of Kenyan stock market based on time series data which consists of daily closing prices of NSE Index for the period 2ndJanuary 2001 to 31st December 2014. The analysis has been done using both symmetric and asymmetric Generalized Autoregressive Conditional Heteroscedastic (GARCH) models. The study provides evidence for the existence of a positive and significant risk premium. Moreover, volatility shocks on daily returns at the stock market are transitory. We do not find any significant leverage effect. Introduction of the new regulations on foreign investors with a 25% minimum reserve of the issued share capital going to local investors (in 2002), introduction of live trading, cross listing in Uganda and Tanzania stock exchange (in 2006) and change in equity settlement cycle from T+4 to T+3 (in 2011) significantly reduce volatility clustering. The onset of US tapering increase the daily mean returns significantly while reducing conditional volatility.