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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.
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Keywords:
- quantum field theory /
- treasury forward interest rate /
- incomplete correlations /
- psychological perceptive remaining time
[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 物理学报 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 物理学报 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 物理学报 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
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[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 物理学报 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 物理学报 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 物理学报 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
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