基于UKF的非齐次泊松跳跃市场微结构模型研究

摘要

本文针对不确定性因素引起资产价格的巨大波动,构建了一个由非齐次泊松过程驱动的跳跃市场微结构模型.在模型参数未知的情况下,我们使用非参数化方法检测出时变跳跃强度,由此再利用无迹卡尔曼滤波和极大似然法来估计跳跃市场微结构模型参数的值.模拟仿真与实证分析验证了该方法的有效性,并利用AIC准则对两类跳跃波动率模型进行了优劣比较.研究结果表明,跳跃市场微结构模型在拟合股指数据方面要优于跳跃随机波动模型.%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.