搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

国债远期利率的量子场理论模型构建

雷丽梅 冯玲

引用本文:
Citation:

国债远期利率的量子场理论模型构建

雷丽梅, 冯玲

The quantum field model for treasury forward interest rate

Lei Li-Mei, Feng Ling
PDF
导出引用
  • 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 quantum field theory to model the term structure of treasury forward rates compared with traditionally used two-factor HJM model in financial industry. In conclusion, the quantum field model we constructed, is more consistent with the actual situation, and all the parameters estimated by this model are obtained directly from the market data, without making any assumption of the specific form of forward rate volatility function, thus greatly improving the accuracy of applying the quantum field theory to finance. These findings are not only of great theoretic and practical significance for applying the quantum field theory to pricing those financial products linked to treasury bonds and for managing its relevant interest rate risk, but also have reference value for quantitatively analyzing banks and finance companies in financial field, and also for practitioners in the field of fixed-income securities.
      通信作者: 冯玲, 332714502@qq.com
    • 基金项目: 国家自然科学基金(批准号:71573043)资助的课题.
      Corresponding author: Feng Ling, 332714502@qq.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 71573043).
    [1]

    Andersen L, Andreasen J 2000 Appl. Math. Financ. 7 1

    [2]

    Henrard M 2010 Wilm. J. 2 135

    [3]

    Beliaeva N, Nawalkha S 2012 J. Bank Financ. 36 151

    [4]

    Chen Z Y, Jiang L 2016 J. Syst. Eng. 31 202 (in Chinese) [陈志勇, 江良 2016 系统工程学报 31 202]

    [5]

    Ma J H, Sun B 2017 Syst. Eng.: Theory Pract. 37 288 (in Chinese) [马俊海, 孙斌 2017 系统工程理论与实践 37 288]

    [6]

    Haven E E 2002 Physica A 304 507

    [7]

    Montagna G, Nicrosini O, Moreni N 2002 Physica A 310 450

    [8]

    Contreras M, Montalva R, Pellicer R, Villena M 2010 Physica A 389 3552

    [9]

    Kim M J, Hwang D I, Lee S Y, Kim S Y 2011 Physica A 390 847

    [10]

    Wu T L, Xu S Q 2014 J. Futur. Mark. 34 580

    [11]

    Fan H 2014 Acta Phys. Sin. 63 038902 (in Chinese) [范宏 2014 63 038902]

    [12]

    Zhou R W, Li J C, Dong Z W, Li Y X, Qian Z W 2017 Acta Phys. Sin. 66 040501 (in Chinese) [周若微, 李江城, 董志伟, 李云仙, 钱振伟 2017 66 040501]

    [13]

    Tang Z P, Chen W H, Ran M 2017 Acta Phys. Sin. 66 120203 (in Chinese) [唐振鹏, 陈尾虹, 冉梦 2017 66 120203]

    [14]

    Tarasov V E, Tarasova V V 2017 Ann. Phys. 383 579

    [15]

    Henkel C 2017 Physica A 469 447

    [16]

    Ma C, Ma Q H, Yao H X, Hou T C 2018 Physica A 494 87

    [17]

    Baaquie B E 2001 Phys. Rev. E 64 016121

    [18]

    Baaquie B E 2002 Phys. Rev. E 65 056122

    [19]

    Baaquie B E 2004 Quantum Finance (Singapore:Cambridge University Press) p147

    [20]

    Baaquie B E 2009 Interest Rates and Coupon Bonds in Quantum Finance (UK:Cambridge University Press) p91

    [21]

    Baaquie B E, Pan T 2012 Physica A 391 1287

    [22]

    Baaquie B E, Du X, Tang P, Cao Y 2014 Physica A 401 182

    [23]

    Baaquie B E, Yu M, Bhanap J 2018 Physica A 492 222

    [24]

    Heath D, Jarrow R, Morton A 1992 Econometrica 60 77

    [25]

    Kennedy D P 1994 Math. Financ. 4 247

    [26]

    Kennedy D P 1997 Math. Financ. 7 107

    [27]

    Goldstein P 2000 J. Financ. Stud. 13 365

    [28]

    Santa-Clara P, Sornette D 2001 Rev. Financ. Stud. 14 149

    [29]

    Kim M L, Hwang D I, Lee S Y, Kim S Y 2011 Physica A 390 847

    [30]

    Amin K I, Morton A J 1994 J. Financ. Econ. 35 141

  • [1]

    Andersen L, Andreasen J 2000 Appl. Math. Financ. 7 1

    [2]

    Henrard M 2010 Wilm. J. 2 135

    [3]

    Beliaeva N, Nawalkha S 2012 J. Bank Financ. 36 151

    [4]

    Chen Z Y, Jiang L 2016 J. Syst. Eng. 31 202 (in Chinese) [陈志勇, 江良 2016 系统工程学报 31 202]

    [5]

    Ma J H, Sun B 2017 Syst. Eng.: Theory Pract. 37 288 (in Chinese) [马俊海, 孙斌 2017 系统工程理论与实践 37 288]

    [6]

    Haven E E 2002 Physica A 304 507

    [7]

    Montagna G, Nicrosini O, Moreni N 2002 Physica A 310 450

    [8]

    Contreras M, Montalva R, Pellicer R, Villena M 2010 Physica A 389 3552

    [9]

    Kim M J, Hwang D I, Lee S Y, Kim S Y 2011 Physica A 390 847

    [10]

    Wu T L, Xu S Q 2014 J. Futur. Mark. 34 580

    [11]

    Fan H 2014 Acta Phys. Sin. 63 038902 (in Chinese) [范宏 2014 63 038902]

    [12]

    Zhou R W, Li J C, Dong Z W, Li Y X, Qian Z W 2017 Acta Phys. Sin. 66 040501 (in Chinese) [周若微, 李江城, 董志伟, 李云仙, 钱振伟 2017 66 040501]

    [13]

    Tang Z P, Chen W H, Ran M 2017 Acta Phys. Sin. 66 120203 (in Chinese) [唐振鹏, 陈尾虹, 冉梦 2017 66 120203]

    [14]

    Tarasov V E, Tarasova V V 2017 Ann. Phys. 383 579

    [15]

    Henkel C 2017 Physica A 469 447

    [16]

    Ma C, Ma Q H, Yao H X, Hou T C 2018 Physica A 494 87

    [17]

    Baaquie B E 2001 Phys. Rev. E 64 016121

    [18]

    Baaquie B E 2002 Phys. Rev. E 65 056122

    [19]

    Baaquie B E 2004 Quantum Finance (Singapore:Cambridge University Press) p147

    [20]

    Baaquie B E 2009 Interest Rates and Coupon Bonds in Quantum Finance (UK:Cambridge University Press) p91

    [21]

    Baaquie B E, Pan T 2012 Physica A 391 1287

    [22]

    Baaquie B E, Du X, Tang P, Cao Y 2014 Physica A 401 182

    [23]

    Baaquie B E, Yu M, Bhanap J 2018 Physica A 492 222

    [24]

    Heath D, Jarrow R, Morton A 1992 Econometrica 60 77

    [25]

    Kennedy D P 1994 Math. Financ. 4 247

    [26]

    Kennedy D P 1997 Math. Financ. 7 107

    [27]

    Goldstein P 2000 J. Financ. Stud. 13 365

    [28]

    Santa-Clara P, Sornette D 2001 Rev. Financ. Stud. 14 149

    [29]

    Kim M L, Hwang D I, Lee S Y, Kim S Y 2011 Physica A 390 847

    [30]

    Amin K I, Morton A J 1994 J. Financ. Econ. 35 141

  • [1] 夏茂鹏, 李健军, 高冬阳, 胡友勃, 盛文阳, 庞伟伟, 郑小兵. 基于相关光子多模式相关性的InSb模拟探测器定标方法.  , 2015, 64(24): 240601. doi: 10.7498/aps.64.240601
    [2] 王林元, 刘宏奎, 李磊, 闫镔, 张瀚铭, 蔡爱龙, 陈建林, 胡国恩. 基于稀疏优化的计算机断层成像图像不完全角度重建综述.  , 2014, 63(20): 208702. doi: 10.7498/aps.63.208702
    [3] 杨富强, 张定华, 黄魁东, 王鹍, 徐哲. CT不完全投影数据重建算法综述.  , 2014, 63(5): 058701. doi: 10.7498/aps.63.058701
    [4] 弭光宝, 李培杰, 黄旭, 曹春晓. 液态结构与性质关系Ⅲ剩余键理论模型.  , 2012, 61(18): 186106. doi: 10.7498/aps.61.186106
    [5] 高湘昀, 安海忠, 方伟. 基于复杂网络的时间序列双变量相关性波动研究.  , 2012, 61(9): 098902. doi: 10.7498/aps.61.098902
    [6] 李凤, 马忠权, 孟夏杰, 殷晏庭, 于征汕, 吕鹏. 晶硅太阳电池中Fe-B对与少子寿命、陷阱浓度及内量子效率的相关性.  , 2010, 59(6): 4322-4329. doi: 10.7498/aps.59.4322
    [7] 王启光, 侯威, 郑志海, 冯爱霞, 邓北胜. 极端事件再现时间长程相关性与群发性研究.  , 2010, 59(10): 7491-7497. doi: 10.7498/aps.59.7491
    [8] 王亚奇, 蒋国平. 复杂网络中考虑不完全免疫的病毒传播研究.  , 2010, 59(10): 6734-6743. doi: 10.7498/aps.59.6734
    [9] 王启光, 侯威, 郑志海, 高荣. 东亚区域大气长程相关性.  , 2009, 58(9): 6640-6650. doi: 10.7498/aps.58.6640
    [10] 封国林, 龚志强, 侯威, 王启光, 支蓉. 气象领域极端事件的长程相关性.  , 2009, 58(4): 2853-2861. doi: 10.7498/aps.58.2853
    [11] 王启光, 支 蓉, 张增平. Lorenz系统长程相关性研究.  , 2008, 57(8): 5343-5350. doi: 10.7498/aps.57.5343
    [12] 张佃中. 非线性时间序列互信息与Lempel-Ziv复杂度的相关性研究.  , 2007, 56(6): 3152-3157. doi: 10.7498/aps.56.3152
    [13] 刘 慧, 张 军. 基于节点相关性的网络不动点理论研究.  , 2007, 56(4): 1952-1957. doi: 10.7498/aps.56.1952
    [14] 程 勇, 张 雄, 伍 林, 毛慰明, 尤莉莎. 用离散相关函数方法分析Blazar天体的γ射线和射电辐射的相关性.  , 2006, 55(2): 988-994. doi: 10.7498/aps.55.988
    [15] 张秋菊, 盛政明, 王兴海, 满宝元, 苍 宇, 张 杰. 相位反射产生的激光场空洞现象及其与激光等离子体参数相关性研究.  , 2006, 55(5): 2347-2351. doi: 10.7498/aps.55.2347
    [16] 李富斌. 由微观随机动力学导出非平衡稳定态的长程相关性(Ⅰ)——用随机点阵气模型构造出宏观涨落流体力学理论.  , 1990, 39(3): 381-390. doi: 10.7498/aps.39.381
    [17] 黎永清, 王育竹. 利用光子相关性降低量子噪声.  , 1989, 38(3): 476-480. doi: 10.7498/aps.38.476
    [18] 罗耕贤, 郭光灿. 双色场Jaynes-Cummings模型的量子理论.  , 1988, 37(12): 1956-1964. doi: 10.7498/aps.37.1956
    [19] 张叔英. 用于信号检测的时间压缩相关器理论分析.  , 1976, 25(3): 235-245. doi: 10.7498/aps.25.235
    [20] 杨泽森. 时间相关的多道散射理论.  , 1963, 19(4): 239-248. doi: 10.7498/aps.19.239
计量
  • 文章访问数:  5655
  • PDF下载量:  115
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-03-12
  • 修回日期:  2018-08-07
  • 刊出日期:  2018-10-05

/

返回文章
返回
Baidu
map