Abstract: Aiming at the huge price fluctuations caused by the market uncertainty, we develop a jump market microstructure model with nonhomogeneous Poisson process. Under the condition of unknown parameters, a new nonparametric method is proposed to detect the time-varying jump intensity. Based on the detected jump, we estimate its parameters by combining the unscented Kalman filter method with the maximum likelihood method. Simulation results and empirical study show the effectiveness of the proposed method. The AIC is used to compare two kinds of volatility models with jump, and the results show that the proposed market microstructure model is superior to the stochastic volatility in fitting the stock index data.

Key words: market microstructure, jump-diffusion model, nonhomogeneous Poisson process, unscented Kalman filter, maximum likelihood method