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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2017, Vol. 34 ›› Issue (3): 232-246.doi: 10.3969/j.issn.1005-3085.2017.03.002

• • 上一篇    下一篇

基于UKF的非齐次泊松跳跃市场微结构模型研究

席燕辉1,2,   彭   辉3,   阮   昌3,   丁美青4   

  1. 1- 长沙理工大学电气与信息工程学院，长沙  410076
    2- 国防科技大学信息系统与管理学院，长沙  410073
    3- 中南大学信息科学与工程学院，长沙  410083
    4- 长沙理工大学交通运输工程学院，长沙  410076
  • 收稿日期:2014-09-10 接受日期:2016-11-17 出版日期:2017-06-15 发布日期:2017-08-15
  • 基金资助:
    国家自然科学基金(51507015)；中国博士后科学基金(2016M592949)；湖南省自然科学基金(2015JJ3008)；湖南省科技计划(2015NK3035)；可再生能源电力技术湖南省重点实验室基金(2014ZNDL002).

Research on Market Microstructure Model with Nonhomogeneous Poisson Jump Based on UKF

XI Yan-hui1,2,   PENG Hui3,   RUAN Chang3,   DING Mei-qing4   

  1. 1- School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410076
    2- College of Information Systems and Management, National University of Defense Technology, Changsha 410073
    3- School of Information Science and Engineering, Central South University, Changsha 410083
    4- School of Traffic and Transportation Engineering, Changsha University of Science and Technology, Changsha 410076
  • Received:2014-09-10 Accepted:2016-11-17 Online:2017-06-15 Published:2017-08-15
  • Supported by:
    The National Natural Science Foundation of China (51507015); China Postdoctoral Science Foundation (2016M592949); the Natural Science Foundation of Hunan Province (2015JJ3008); the Science and Technology Program of Hunan Province (2015NK3035); the Fund of  Key Laboratory of Renewable Energy Electric-Technology of Hunan Province (2014ZNDL002).

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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．

关键词: 市场微结构, 跳跃扩散模型, 非齐次泊松过程, 无迹卡尔曼滤波, 极大似然法

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

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