A Difference Equation of Banking Loan with Nonlinear Deposit Interest Rate

Year 2024, , 14 - 19, 08.05.2024

Moch. Fandi Ansori , F. Hilal Gümüş

https://doi.org/10.33187/jmsm.1396368

Abstract

This paper considers a banking loan model using a difference equation with a nonlinear deposit interest rate. The construction of the model is based on a simple bank balance sheet composition and a gradient adjustment process. The model produces two unstable loan equilibriums and one stable equilibrium when the parameter corresponding to the deposit interest rate is situated between its transcritical and flip bifurcations. Some numerical simulations are presented to align with the analytical findings, such as the bifurcation diagram, Lyapunov exponent, cobweb diagram, and contour plot sensitivity. The significance of our result is that the banking regulator may consider the lower and upper bounds for setting the nonlinear interest rate regulation and provide a control regulation for other banking factors to maintain loan stability.

Keywords

Banking loan dynamics, Nonlinear interest rate, Stability

References

• [1] M. F. Ansori, S. Hariyanto, Analysis of banking deposit cost in the dynamics of loan: Bifurcation and chaos perspectives, BAREKENG: J. Math. App., 16(4) (2022), 1283-1292, doi:10.30598/barekengvol16iss4pp1283-1292.
• [2] M. F. Ansori, S. Khabibah, The role of cost of loan in banking loan dynamics: Bifurcation and chaos analysis, BAREKENG: J. Math. App., 16(3) (2022), 1031-1038, doi:10.30598/barekengvol16iss3pp1031-1038.
• [3] N. Y. Ashar, M. F. Ansori, H. K. Fata, The effects of capital policy on banking loan dynamics: A difference equation approach, Int. J. Differ. Equations (IJDE), 18(1) (2023), 267-279.
• [4] H. K. Fata, N. Y. Ashar, M. F. Ansori, Banking loan dynamics with dividen payments, Adv. Dyn. Syst. Appl. (ADSA), 18(2) (2023), 87-99.
• [5] M. F. Ansori, G. Theotista, Winson, Difference equation-based banking loan dynamics with reserve requirement policy, Int. J. Differ. Equations (IJDE), 18(1) (2023), 35-48.
• [6] M. F. Ansori, N. Sumarti, K. A. Sidarto, I. Gunadi, Analyzing a macroprudential instrument during the COVID-19 pandemic using border collision bifurcation, Rect@: Rev. Electron. Commun. y Trabajos de ASEPUMA, 22(2) (2022), 113-125, doi: 10.24309/recta.2021.22.2.04.
• [7] M. F. Ansori, G. Theotista, M. Febe, The influence of the amount of premium and membership of IDIC on banking loan procyclicality: A mathematical model, Adv. Dyn. Syst. Appl. (ADSA), 18(2) (2023), 111-123.
• [8] M. F. Ansori, N. Y. Ashar, Analysis of loan benchmark interest rate in banking loan dynamics: bifurcation and sensitivity analysis, J. Math. Model. Finance, 3(1) (2023), 191-202, doi: 10.22054/jmmf.2023.74976.1098.
• [9] L. Fanti, The dynamics of a banking duopoly with capital regulations, Econ. Model., 37 (2014), 340-349, doi: 10.1016/j.econmod.2013.11.010.
• [10] S. Brianzoni, G. Campisi, Dynamical analysis of a banking duopoly model with capital regulation and asymmetric costs, Discrete Contin. Dyn. Syst. - B, 26 (2021), 5807-5825, doi: 10.3934/dcdsb.2021116.
• [11] S. Brianzoni, G. Campisi, A. Colasante, Nonlinear banking duopoly model with capital regulation: The case of Italy, Chaos Solitons Fractals, 160 (2022), 112209, doi: 10.1016/j.chaos.2022.112209.
• [12] G. A. Pfann, P. C. Schotman, R. Tschernig, Nonlinear interest rate dynamics and implications for the term structure, J. Econom., 74(1) (1996), 149-176, doi: 10.1016/0304-4076(95)01754-2.
• [13] L. Ballester, R. Ferrer, C. Gonz´alez, Linear and nonlinear interest rate sensitivity of Spanish banks, The Spanish Rev. Financ. Econ., 9(2) (2011), 35-48, doi: 10.1016/j.srfe.2011.09.002.
• [14] P. A. Shively, Threshold nonlinear interest rates, Econ. Lett., 88(3) (2005), 313-317, doi: 10.1016/j.econlet.2004.12.032.
• [15] Y. Baaziz, M. Labidi, A. Lahiani, Does the South African reserve bank follow a nonlinear interest rate reaction function?, Econ. Model., 35 (2005), 272-282, doi: 10.1016/j.econmod.2013.07.014.
• [16] R. Br¨uggemann, J. Riedel, Nonlinear interest rate reaction functions for the UK, Econ. Model., 28 (2011), 1174-1185, doi: 10.1016/j.econmod.2010.12.005.
• [17] M. A. Klein, A theory of the banking firm, J. Money Credit Banking, 3 (1971), 205-218.
• [18] M. Monti, Deposit, credit and interest rates determination under alternative objective functions, G. P. Szego, K. Shell (Eds.), Math. Methods Investment Finance, Amsterdam, 1972.
• [19] M. G. I. Bischi, C. Chiarella, M. Kopel, F. Szidarovszky, Nonlinear Oligopolies: Stability and Bifurcations, Berlin: Springer-Verlag, 2010.
• [20] S. Elaydi, An Introduction to Difference Equations, New York, NY, USA: Springer, 1996.
• [21] K. Alligood, T. Sauer, J. Yorke, Chaos: An Introduction to Dynamical Systems, New York: Springer-Verlag, 1996.
• [22] M. F. Ansori, N. Y. Ashar, H. K. Fata, Logistic map-based banking loan dynamics with central bank policies, J. Appl. Nonlinear Dyn., (2024), (in press).