Statistical Analysis Of Asymmetric Two-parameter And Three-parameter Laplace Distribution

The distribution of stock index return is an important issue in financial research.Research on the distribution of stock index return not only helps investors to understand the inherent laws of the stock market,but also helps investors in stock index futures to make the right risk measure for asset pricing and portfolio selection.The distribution of financial assets and the statistical analysis of financial assets is one of the most important issues in financial research.This paper gives the statistical analysis of the asymmetric two parameter Laplace distribution.We use the method of moment estimation and maximal likelihood to estimate the parameters.It is proved that the result of maximum likelihood estimation method is consistent with the result of the second method of moment estimation.Monte-Carlo simulation is used to compare those estimation methods,it is concluded that the accuracy of the second method of moment estimation is better.Then this paper gives the statistical analysis and parameter estimation of asymmetric three parameter Laplace distribution.The existing literatures show that the parameter estimation of the asymmetric three parameter Laplace distribution is obtained by the method of maximum likelihood,but the existence and uniqueness theory of the maximal likelihood estimation are not complete.This article gives a relatively simple approach.Finally,the paper fits daily and weekly stock index return data in Shanghai Composite Index and Shenzhen Component Index using asymmetric Laplace distribution.It concludes that asymmetric Laplace distribution is better fitted than normal distribution about the characteristics of leptokurtic,heavy tail,skewness.When we choose the distribution of stock index return,asymmetric Laplace distribution will be a better choice for stock index risk manager.