国债远期利率的量子场理论模型构建  

The quantum field model for treasury forward interest rate

作　　者：雷丽梅 冯玲 Lei Li-Mei;Feng Lingt(School of Economics and Management,Fuzhou University,Fuzhou 350002,China)

机构地区：[1]福州大学经济与管理学院,福州350002

出　　处：《物理学报》2018年第19期98-109,共12页Acta Physica Sinica

基　　金：国家自然科学基金(批准号:71573043)资助的课题~~

摘　　要：随着我国利率市场化改革的全面推进和利率衍生品数量的增加,如何对远期利率进行精确与合理建模,就显得十分重要和紧迫.本文利用金融物理学中可有效纳入日历时间和到期时间两个维度上的国债远期利率之间不完全相关性的量子场论方法,对2011年1月4日到2016年12月30日的国债瞬时远期利率的实际市场演化进行建模,并将其结果与传统金融只能考虑日历时间方向上的相关性的主流两因子Heath-Jarrow-Morton (HJM)模型的实证结果进行比较.研究结果表明,考虑心理感知剩余时间变量后的量子场理论模型,提供了对实际的国债远期利率的92.67%的拟合优度,优于经典的最优两因子HJM模型69.02%的拟合精度.此外,分别将估计所得的最优参数代入最优量子场理论模型和两因子HJM模型下的远期利率更新方程,对2017年1月3日到2017年12月30日的100个期限的瞬时远期利率的250个瞬时远期利率的期限结构进行回测检验,从平均瞬时远期利率、均方根误差和Theil不等系数三个方面的结果均显示出量子场理论模型对国债远期利率建模的优越性.这些结果对将量子场理论引入到以国债为标的各种金融产品的定价和相关的利率风险管理、银行和金融公司的量化分析以及固定收益证券领域的实践者们均具有重要意义.With the further reform of interest rate liberalization and the increasing of interest rate derivatives, it becomes more important and urgent to model the forward rate accurately and rationally in China. In this paper, we use the quantum field theory in econophysics, which can effectively incorporate the incomplete correlations between forward interest rates with different maturities, to model the Chinese treasury bond instantaneous forward rates. Firstly, we start with the correlation structure of the instantaneous change of treasury forward rates, one of the most important variables for a quantum field, during the period from January 4, 2011 to December 30, 2016, then apply the quantum field theory to model the actual market evolution of the treasury instantaneous forward rates directly. Secondly, we also use the mainstream two-factor Heath-Jarrow-Morton（HJM） model commonly used in financial industry, which requires the particular form of forward rate volatility functions to be set in advance, to model the treasury instantaneous forward rates, then compare the results with those of the quantum field model. The empirical results show that the quantum field model based on stiff action provides a fitting accuracy of 63.23% for actual treasury bond instantaneous forward rate, but this fitting accuracy increases to 92.67% for the quantum field model with taking into account the psychological perceptive remaining time, which is also superior to the classic optimal two-factor HJM model with a fitting accuracy of 69.02%. Finally, the optimal parameters estimated are respectively substituted into the forward interest rate update equations of the quantum field model with the psychological perception time in mind and the classical two-factor HJM model to conduct the back testing of forward rates with one hundred maturities, from January 3, 2017 to December 30,2017. From the results of average instantaneous forward rate, root mean square error and Theil inequality coefficient,we can see the superiority of using the qua

关 键 词：量子场理论 国债远期利率 不完全相关性 心理感知剩余时间 

分 类 号：O413[理学—理论物理]