The study is to understand the volatility linked between Nifty index and Nifty derivative segment i.e. Nifty futures and options while applying the Arch and Garch(1,1)model of time series. The study uses the daily closing price of Nifty index and Nifty future and option contract traded price of both the exchanges and period taken for analysis before and after the pioneer of nifty future and options were introduced is (1996-2000) and (2000-2020) for futures and (2001-2020) for options. This paper aims to analyse the volatility of the market with the linkage between NSE and nifty derivative segment, it helps the investor to better understand the market scenario and its implementation for investors.