Modeling Of Microstructure Nonlinear Dynamics Of Financial Market And Numerical Simulation Based On State Space Method

The microstructure dynamics of finance market is a newly developed research branch. With the multi-disciplinary integration, some economists and financial experts having physics background have proposed new microstructure models of finance market based on the spirit of the phenomenology. The paper performs the research based on the famous Bouchaud and Cont's model.This paper precedes the research mainly from three aspects. Firstly it introduces the simplest discrete microstructure model. For the sake of its nonlinear characteristic, the paper adapts the Extended Kalman Filter (EKF) to perform parameter estimation and state identification. Under the condition of the observability satisfied, by using one measurement equation and two measurement equations separately, the paper finds that if taking more information into consideration the result will be more accurate for a stochastic system. Finally the paper performs comparison with the typical GARCH model.Secondly, the paper investigates the microstructure model with a homogeneous Poisson item on the ground of the simplest model. It is reasonable to add this new jump item given that there are often discontinue price motions in the finance market. The paper uses the Monte Carlo Markov Chain (MCMC) method to detect the jump occurrence in time series and checks the method validation with the simulate data. Then the result of the parameter estimation is given out.At last the paper works on the model with an inhomogeneous Poisson item. Some references have shown that there exists jump cluster situation in the finance market, so it is a better choice to model with an inhomogeneous Poisson item. The present paper uses a new non-parameter detection method to detect the jump. Also simulate data are generated to check the method validation. Parameter estimation and state identification are done by EKF at the end.