基于GMM方法跳聚集的短期利率模型参数估计  

Based on GMM Parametric Estimation for Short Term Interest Model with Jump Cluster

作　　者：张新军 江良[1,2] 林志兴 ZHANG Xinjun;JIANG Liang;LIN Zhixing(School of Mathematics and Finance, Putian University, Putian 351100;Key Laboratory of Financial Mathematics of Fujian Province University, Putian University, Putian 351100)

机构地区：[1]莆田学院数学与金融学院,莆田351100 [2]莆田学院金融数学福建省高校重点实验室,莆田351100

出　　处：《系统科学与数学》2019年第1期90-105,共16页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金项目(11471175);福建省自然科学基金(2016J01677;2017J01565);福建省中青年教师教育科研项目(JAT170500)资助课题

摘　　要：构建具有自我激励机制跳的短期利率模型,应用随机跳的强度来描述自我激励机制跳的过程,即当短期利率发生跳时,同时跳的强度也相应地发生跳,从而刻画跳的聚集现象.文章将以美国国债收益率作为研究目标,通过广义矩估计方法(GMM)给出了模型的参数估计和统计推断.借鉴随机微分算子Taylor展开方法,从理论上给出了精确的矩函数,并通过辅助粒子滤波器(APF)给出随机跳的强度估计.实证结果揭示了文章所构建的模型不仅能够很好地刻画极端事件对于短期利率的冲击,而且也很好地描述跳的聚集现象.此外,实证结果也表明了跳的强度可作为市场压力测试的一个重要指标.This paper proposes a short-term interest model with the self-exciting jump process described by stochastic jump intensity. In the model, a jump of shortterm interests increases the intensity of jumps during the same period, which captures the jump cluster. After researching into U.S. T-Bill rate, this paper will also make parametric estimations and statistical inference through employing the Generalized Moment Method(GMM). The moment function will be theoretically provided under the framework of the stochastic Taylor expansion of the differential operator.Meanwhile, the filtered values of the stochastic jump intensity will be estimated by applying the auxiliary particle filter algorithm(APF). The empirical results show that the model established not only sufficiently describes the impact of the extreme event on short-term interest, but also characterizes the jump cluster phenomena. In addition, the filtered jump intensity is an important indicator of financial market stress measurement.

关 键 词：短期利率模型 跳 Hawkes过程 广义矩估计方法 

分 类 号：F224[经济管理—国民经济] F830