*Assistant Professor,
**Research Scholar, ICSSR Doctoral Fellowship,
The Government of India was open a gate to the foreigners to invest their money in India stock market through globalisation. The FII inflows have steadily grown after liberalization period in India. The foreign investments and capital markets performance are the indicators of industry and economy of a particular country. The stock market developments and their changes had happened only through their loyal investor's participation. So the researcher has to check the volatility in Bombay stock exchange by BSE Sensex return due to FII by using ARCH and GRACH volatility model. Here the researcher uses data of time series econometric model for the 2005–2006 to 2013–2014.