Based on FIGARCH and STGARCH model,a new kind of asymmetric GARCH family model,called STFIGARCH,was introduced to study the warrants market.First of all,the autoregressive conditional heteroskedasticity (ARCH) effect and the long memory rescaled range (R/S) of two stocks' daily return series were tested.A fractionally integrated GARCH (FIGARCH) model and a smooth transition FIGARCH (STFIGARCH) model were established and the estimatioins by these two models were compared and analysed.The results show that there may co-exist both long memory and smooth transition type nonlinearities.Then,the FIGARCH and STFIGARCH option pricing model were established.The empirical results show that the STFIGARCH option pricing model is better than the FIGARCH option pricing model.However,the warrants market tends to be overestimated in the early warrants duration,and with the date of exercise being closer,the price of the Warrants get closer to the theoretical price of model.