均值函数对随机波动率短期利率模型的影响分析  

Impact analysis of mean reverting function to short term rate model with stochastic volatilities

作　　者：江良 林鸿熙[3] 宋丽平 Jiang Liang;Lin Hongxi;Song Liping(School of Mathematics and Finance,Putian University,Putian 351100,China;Key Laboratory of Financial Mathematics of Universities in Fujian Province,Putian University,Putian 351100,China;School of Business,Putian University,Putian 351100,China)

机构地区：[1]莆田学院数学与金融学院,福建莆田351100 [2]福建省高校金融数学重点实验室(莆田学院),福建莆田351100 [3]莆田学院商学院,福建莆田351100

出　　处：《系统工程学报》2018年第5期662-673,共12页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(11471175);福建省自然科学基金资助项目(2015J05012; 2016J01677);莆田学院育苗基金资助项目(2014060; 2014061)

摘　　要：构建均值函数随机波动率短期利率模型,利用核估计和Kalman滤波器给出拟极大似然估计方法.实证结果表明引入均值函数改善了模型的似然率估计值,也减少了随机波动率估计值,同时对衍生品价格也产生较大的影响.这些结果揭示了均值函数对于短期利率模型的冲击较大.此外,也发现不同均值函数模型之间对于衍生价格影响还是比较显著的,而比较常系数模型之间所得衍生价格差异比较小.This paper presents a short term rate model with mean revering function and stochastic volatilities （ESV）. The quasi-maximum likelihood （QML） estimator is developed by using kernel estimator and Kalman filter. The empirical evidences support that the likelihood function will be improved and the estimates of the stochastic volatilities will also dramatically decrease for our ESV model, compared with the constant mean- reverting （CSV）. Meanwhile, the mean revering function affects contingent claims pricing. These implies that the mean revering function has a substantial impact on the dynamic process of short term rate. Moreover, there are slight differences between the prices of the contingent claims of short term rates given by the CSV models, but there are obvious differences between the prices given by ESV models.

关 键 词：均值函数 随机波动率 核估计方法 KALMAN滤波器 

分 类 号：F830.9[经济管理—金融学] O212.7[理学—概率论与数理统计]