Non-Gaussian distribution for stock returns and related stochastic differential equation

Abstract

Daily returns of stock prices are observed to have heavy-tailed and non-central distribution. In this paper, we adopt the type VII and IV family of Pearson System to express the daily returns of stock prices. Furthermore, we consider related stochastic differential equation whose stationary distribution are the type VII or IV of Pearson system, and estimate the parameters of stochastic differential equation by maximum likelihood method, where the transition probability density function and local linearization method are used. This paper is the basic research for the risk management.