Static term structure of interest rate construction with tension interpolation splines

Xiangbin Qin; Yuanpeng Zhu; Xiangbin Qin; Yuanpeng Zhu

doi:10.3934/math.2024014

AIMS Mathematics

2024, Volume 9, Issue 1: 240-256. doi: 10.3934/math.2024014

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Research article

Static term structure of interest rate construction with tension interpolation splines

Xiangbin Qin ¹,
Yuanpeng Zhu ^{2
,
,}

1.
School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China; qinxiangbin@ctbu.edu.cn
2.
School of Mathematics, South China University of Technology, Guangzhou 510640, China

Received: 16 August 2023 Revised: 03 November 2023 Accepted: 12 November 2023 Published: 27 November 2023
MSC : 65D05, 65D17

Traditional theories of term structure of interest rate consist of four major classical theories, including Pure Expectation Theory, Liquidity Preference Theory, Preferred Habitat Theory and Market Segmentation Theory. However, they cannot be well interpreted by the traditional static term structure of interest rate methods such as polynomial spline and exponential spline. To address problems on low precision and weak stability of traditional methods in constructing static interest rate term structure curve, in this paper, we introduce the tension interpolation spline based on a fourth-order differential equation with local tension parameters calculated by Generalized Reduced Gradient (GRG) algorithm. Our primary focus is to illustrate its better prediction effect and stability with an empirical study conducted using datum of treasury bonds. Then, we divided the datum into intra-sample datum for estimating tension parameters and out-of-sample datum for evaluating their robustness of predicting stochastics collected from Shanghai Stock Exchange on $ {2^{{\rm{nd}}}} $ February, 2019. According to the principle of total least squares and total least absolute deviations, the result shows that the tension interpolation spline model has better precision and stronger stability in prediction of out-of-sample treasury bonds prices compared with the model established by polynomial spline and exponential spline. In addition, it can better explain the Liquidity Preference Theory, which confirms that it is suitable for constructing the static term structure of interest rates in the securities exchange market.
- discount curves,
- yield curves,
- static term structure of interest rate,
- treasury bonds pricing,
- Generalized Reduced Gradient,
- tension interpolation spline
Citation: Xiangbin Qin, Yuanpeng Zhu. Static term structure of interest rate construction with tension interpolation splines[J]. AIMS Mathematics, 2024, 9(1): 240-256. doi: 10.3934/math.2024014

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Abstract

Traditional theories of term structure of interest rate consist of four major classical theories, including Pure Expectation Theory, Liquidity Preference Theory, Preferred Habitat Theory and Market Segmentation Theory. However, they cannot be well interpreted by the traditional static term structure of interest rate methods such as polynomial spline and exponential spline. To address problems on low precision and weak stability of traditional methods in constructing static interest rate term structure curve, in this paper, we introduce the tension interpolation spline based on a fourth-order differential equation with local tension parameters calculated by Generalized Reduced Gradient (GRG) algorithm. Our primary focus is to illustrate its better prediction effect and stability with an empirical study conducted using datum of treasury bonds. Then, we divided the datum into intra-sample datum for estimating tension parameters and out-of-sample datum for evaluating their robustness of predicting stochastics collected from Shanghai Stock Exchange on $ {2^{{\rm{nd}}}} $ February, 2019. According to the principle of total least squares and total least absolute deviations, the result shows that the tension interpolation spline model has better precision and stronger stability in prediction of out-of-sample treasury bonds prices compared with the model established by polynomial spline and exponential spline. In addition, it can better explain the Liquidity Preference Theory, which confirms that it is suitable for constructing the static term structure of interest rates in the securities exchange market.

References

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