Undergraduate Research and Creative Activities Journal

We have been presented the properties of asset return by simulation within the empirical data. However, is it possible to illustrate properties by statistical analysis? Most currently existing models fail to reproduce all these statistical features. In this paper, we will elaborate the properties by applying different statistical models: Geometric Brownian Motion and Ehrenfest URN. We will focus on the following properties: distributional properties, tail properties and extreme fluctuations, path-wise regularity, linear and nonlinear dependence of returns in time and across stocks. In this project, I will use S&P 500 index return as the data and apply it with the models to compare the results with empirical data.