This paper investigates daily stock market volatility of 9 developed and 11 emerging stock markets of the world using different symmetnc, as well as asymmetric GARCH models. The symmetric GARCH parameters suggest that though market behaves differently for different countries in terms of reaction and persistence in volatility, the return generating process in all markets is charactenzed by a high degree of persistence in conditional variance. The estimated parameters of TGARCH model reveal that in all markets, volatility is an asymmetric function of past innovation. Finally, the results of TGARCH-M model indicate insignificant risk-return relationship of most of the markets.