The Estimation of the Parameter of Stable Distribution

There are many distributions to fit the financial data, stable distribution is one kind of distribution classes which can better describe the financial data with heavy tail and excess kurtosis. It is very difficult to estimate the parameter of the stable distribution by the classical estimation methods for there is no direct density function and the first or higher moments may not exist. We develop a new parametric estimation similar as the Duffie and Singleton （1993）’s Simulation Moments Method （SMM） and discuss the property of the new estimator. Finally, we give a example of Shen Zhen composition index using our methods.