Abstract: This paper introduces a type of Levy tempered stable distributions for financial assets return,and some properties of those distributions along with the advatages in applying them to finance assets prices process modeling will be discussed. Direct maximum likelihood estimation is usually impossible for most of continuous-time models in finance except some special cases since it is hard for these models to have analytical form for probility density function. Because characteristic function is equivalent to probility density function,estimation conducted by characteristic function based on GMM with a continuum of moment conditions(CF-CGMM) is developed in this paper. According to the data of HANG SENG INDEX,SSE Composite Index and S &P500 Index,emperical research on these Levy tempered stable distributions are done with the estimations by the CF-CGMM methods,and then statistics measuring and goodness of fit for the models are completed. Moreover the paper also gives some realistic interpretations about the price process of HANG SENG INDEX、SSE Composite Index and S &P500 Index based on the different parameters in Levy tempered stable distribution and emperical results.

Key words: Levy tempered stable distributions, characteristic function, jump, continuum of moment conditions, GMM, estimations