Modeling Complicated Behavior of Stock Prices Using Discrete Self-Excited Multifractal Process

It is usually a challenge for finance and financial engineering to quantitatively describe the complicated behavior of stock prices because the behavior is caused by the adaptability and reflexivity of investors, driven by the endogenous interaction and perturbed by exogenous news. This paper models the behavior of stock prices basing on Self-excited multifractal(SEMF) process and deduces that probability distributions of the model are exponentially tempered Pareto distributions(CGMY model).The maximum likelihood estimator can be used to estimate parameters of CGMY and SEMF. The empirical results demonstrate that the SEMF process have a very good ability to quantitatively describe the complicated behavior of stock prices.