Document Type : Research Article

Authors

Department of Mathematics, Faculty of Science and Mathematics, Universitas Diponegoro

Abstract

One of central bank regulations that has direct impact on the banking industry is loan benchmark interest rate. Banks use it as a reference rate to determine their loan interest rate. In this paper, we study the role of loan benchmark interest rate on banking loan dynamics. The model is in the form of a difference equation that follows a gradient adjustment process. We study the loan equilibrium's stability via bifurcation theory. It is found that the benchmark rate must be set between the flip and transcritical values. Some numerical simulations are performed to confirm the analytical result. The stochastic case of the benchmark rate is also studied. In addition, we perform numerical sensitivity analysis of the benchmark rate with the model's other parameters.

Keywords

###### ##### References
[1] K. Alligood, T. Sauer, and J. Yorke, Chaos: An introduction to dynamical systems, SpringerVerlag, New York, 1996.
[2] M. F. Ansori and S. Hariyanto, Analysis of banking deposit cost in the dynamics of loan: Bifurcation and chaos perspectives, BAREKENG: Journal of Mathematics and Its Application
16 (2022), no. 4, 1283–1292.
[3] M. F. Ansori and S. Khabibah, The role of cost of loan in banking loan dynamics: Bifurcation
and chaos analysis, BAREKENG: Journal of Mathematics and Its Application 16 (2022),
no. 3, 1031–1038.
[4] M. F. Ansori, G. Theotista, and Winson, Difference equation-based banking loan dynamics
with reserve requirement policy, International Journal of Difference Equations 18 (2023), no. 1,
35–48.
[5] M.F. Ansori, K.A. Sidarto, and N. Sumarti, Logistic models of deposit and loan between
two banks with saving and debt transfer factors, AIP Conference Proceedings 2192 (2019),
060002–1–060002–10.
[6] , Model of deposit and loan of a bank using spiral optimization algorithm, Journal of the
Indonesian Mathematical Society 25 (2019), no. 3, 292–301.
[7] M.F. Ansori, K.A. Sidarto, N. Sumarti, and I. Gunadi, Dynamics of bank’s balance sheet: A
system of deterministic and stochastic differential equations approach, International Journal
of Mathematics and Computer Science 16 (2021), no. 3, 871–884.
[8] M.F. Ansori, N. Sumarti, K.A. Sidarto, and I. Gunadi, An algorithm for simulating the
banking network system and its application for analyzing macroprudential policy, Computer
Research and Modeling 13 (2021), no. 6, 1275–1289.
[9] , Analyzing a macroprudential instrument during the covid-19 pandemic using border collision bifurcation, Revista Electronica de Comunicaciones y Trabajos de ASEPUMA: Rect@
22 (2021), no. 2, 113–125.
[10] M.F. Ansori, G. Theotista, and M. Febe, The influence of the amount of premium and membership of idic on banking loan procyclicality: A mathematical model, Advances in Dynamical
Systems and Applications 18 (2023), no. 2, 111–123.
[11] M. Aquilina, G. Ibikunle, V. Mollica, and T. Steffen, The visible hand: benchmarks, regulation, and liquidity, Journal of Financial Markets (2022), 100734.
[12] N.Y. Ashar, M.F. Ansori, and H.K. Fata, The effects of capital policy on banking loan
dynamics: A difference equation approach, International Journal of Difference Equations
(2023), Accepted.
[13] P. Augustin, M. Chernov, L. Schmid, and D. Song, Benchmark interest rates when the
government is risky, Journal of Financial Economics 140 (2021), no. 1, 74–100.
[14] G.I. Bischi, C. Chiarella, M. Kopel, and F. Szidarovszky, Nonlinear oligopolies: Stability and
bifurcations, Springer-Verlag, 2010.
[15] S. Brianzoni and G. Campisi, Dynamical analysis of a banking duopoly model with capital
regulation and asymmetric costs, Discrete and Continuous Dynamical Systems - B 26 (2021),
no. 11, 5807–5825.
[16] S. Brianzoni, G. Campisi, and A. Colasante, Nonlinear banking duopoly model with capital
regulation: The case of italy, Chaos, Solitons and Fractals 160 (2022), 112209.
[17] Q. Duan, Y. Wei, and Z. Chen, Relationship between the benchmark interest rate and a
macroeconomic indicator, Economic Modelling 38 (2014), 220–226.
[18] L. Fanti, The dynamics of a banking duopoly with capital regulations, Economic Modelling
37 (2014), 340–349.
[19] H.K. Fata, N.Y. Ashar, and M.F. Ansori, Banking loan dynamics with dividend payments,
Advances in Dynamical Systems and Applications 18 (2023), no. 2, 97–99.
[20] G. Gandolfo, Economic dynamics: Methods and models, 2 ed., Elsevier Science Publisher
BV, Amsterdam, 1985.
[21] I. Gunadi and C.A. Harun, Revitalising reserve requirement in banking model: An industrial
organisation approach, SEACEN Occasional Papers (2011), no. 51.
[22] H. Kim and W. Shi, The determinants of the benchmark interest rates in china, Journal of
Policy Modeling 40 (2018), no. 2, 395–417.
[23] M.A. Klein, A theory of the banking firm, Journal of Money, Credit, and Banking 3 (1971),
205–218.
[24] M. Monti, Deposit, credit and interest rates determination under alternative objective functions, Mathematical methods in investment and finance (Amsterdam) (G.P. Szego and
K. Shell, eds.), Elsevier Science Publisher BV, 1972.