This research report uses arch and g ARCH models to investigate the influence of introducing index futures derivatives and index option derivatives on obtaining the periodic data of time-varying fluctuations in Indian stock market from June 1995 to July 2006. The reported research results, the loveliness of introducing index futures and index options, have not obtained any structural change conditions, but the loveliness of turbulence. However, after the market efficiency was improved, the derivatives were introduced. The conclusion is that financial derivatives irresponsibly increase or decrease the volatility of the spot market, but there may be some other market factors that affect the market volatility.