ANALYSIS OF BANKING DEPOSIT COST IN THE DYNAMICS OF LOAN: BIFURCATION AND CHAOS PERSPECTIVES
Abstract
A dynamic model of banking loan based on the gradient adjustment process is presented. The amount of loan that will be channeled in the future depends on the sign of the marginal profit of loan. In this paper, we study the deposit cost in the dynamics of a bank’s loan using bifurcation theory. The analysis shows that the deposit cost can affect the stability of loan equilibrium. If the deposit cost is too high, then the loan equilibrium can lose its stability trough transcritical bifurcation. Meanwhile, if the deposit cost is too low, then the loan equilibrium may lose its stability via flip bifurcation and road to chaos. The loan equilibrium stable if the deposit cost is in between the bifurcation values. These findings are confirmed by the numerical simulations. In addition, we present the graph of Lyapunov exponent to see the existence of chaos and the graph of chaotic loan that is sensitive to the initial condition.
Downloads
References
G. E. Chortareas, C. Girardone, and A. Ventouri, “Financial freedom and bank efficiency: Evidence from the European Union,” J. Bank. Financ., vol. 37, no. 4, pp. 1223–1231, Apr. 2013, doi: 10.1016/J.JBANKFIN.2012.11.015.
S. Yamazaki and H. Miyamoto, “A Note on Bank Behavior and Monetary Policies in an Oligopolistic Market,” 2004.
K. Matthews and J. Thompson, The economics of banking. 2nd ed. 2008.
M. F. Ansori, N. Sumarti, K. A. Sidarto, and I. Gunadi, “Dynamics of Bank’s Balance Sheet: A System of Deterministic and Stochastic Differential Equations Approach,” Int. J. Math. Comput. Sci., vol. 16, no. 3, pp. 871–884, 2021.
S. Brianzoni and G. Campisi, “Dynamical analysis of a banking duopoly model with capital regulation and asymmetric costs,” Discret. Contin. Dyn. Syst. - Ser. B, vol. 26, no. 11, pp. 5807–5825, 2021, doi: 10.3934/DCDSB.2021116.
S. Brianzoni, G. Campisi, and A. Colasante, “Nonlinear banking duopoly model with capital regulation: The case of Italy,” Chaos, Solitons & Fractals, vol. 160, p. 112209, Jul. 2022, doi: 10.1016/J.CHAOS.2022.112209.
M. C. V. Manlagñit, “Cost efficiency, determinants, and risk preferences in banking: A case of stochastic frontier analysis in the Philippines,” J. Asian Econ., vol. 22, no. 1, pp. 23–35, Feb. 2011, doi: 10.1016/J.ASIECO.2010.10.001.
G. Chortareas, G. Kapetanios, and A. Ventouri, “Credit market freedom and cost efficiency in US state banking,” J. Empir. Financ., vol. 37, pp. 173–185, Jun. 2016, doi: 10.1016/J.JEMPFIN.2016.03.002.
Y. D. Deli, M. D. Delis, I. Hasan, and L. Liu, “Enforcement of banking regulation and the cost of borrowing,” J. Bank. Financ., vol. 101, pp. 147–160, Apr. 2019, doi: 10.1016/J.JBANKFIN.2019.01.016.
E. Lee, C. Kim, and M. A. Leach-López, “Banking competition and cost stickiness,” Financ. Res. Lett., vol. 41, p. 101859, Jul. 2021, doi: 10.1016/J.FRL.2020.101859.
W. Li and K. Zheng, “Product market competition and cost stickiness,” Rev. Quant. Financ. Account., vol. 49, no. 2, pp. 283–313, 2017.
A. R. Fonseca and F. González, “How bank capital buffers vary across countries: The influence of cost of deposits, market power and bank regulation,” J. Bank. Financ., vol. 34, no. 4, pp. 892–902, Apr. 2010, doi: 10.1016/J.JBANKFIN.2009.09.020.
B. Zhu and Y. Zhao, “Carbon risk and the cost of bank loans: Evidence from China,” Technol. Forecast. Soc. Change, vol. 180, p. 121741, Jul. 2022, doi: 10.1016/J.TECHFORE.2022.121741.
W. C. Chiu, T. H. D. King, and C. W. Wang, “Debt maturity dispersion and the cost of bank loans,” J. Corp. Financ., vol. 70, p. 102049, Oct. 2021, doi: 10.1016/J.JCORPFIN.2021.102049.
I. Hasan, S. J. Kim, P. N. Politsidis, and E. Wu, “Loan syndication under Basel II: How do firm credit ratings affect the cost of credit?,” J. Int. Financ. Mark. Institutions Money, vol. 72, p. 101331, May 2021, doi: 10.1016/J.INTFIN.2021.101331.
E. Dalla and E. Varelas, “Regulation & oligopoly in banking: The role of banking cost structure,” J. Econ. Bus., vol. 104, p. 105836, Jul. 2019, doi: 10.1016/J.JECONBUS.2019.02.002.
X. Hou, S. Li, P. Guo, and Q. Wang, “The cost effects of shadow banking activities and political intervention: Evidence from the banking sector in China,” Int. Rev. Econ. Financ., vol. 57, pp. 307–318, Sep. 2018, doi: 10.1016/J.IREF.2018.01.019.
M. Quijano, “Financial fragility, uninsured deposits, and the cost of debt,” North Am. J. Econ. Financ., vol. 24, no. 1, pp. 159–175, Jan. 2013, doi: 10.1016/J.NAJEF.2012.10.001.
M. F. Ansori and S. Khabibah, “The role of cost of loan in banking loan dynamics: Bifurcation and chaos analysis,” BAREKENG J. Math App., vol. 16, no. 3, pp. 1031–1038, 2022, doi: 10.30598/barekengvol16iss3pp1031-1038.
A. A. Elsadany, “Dynamics of a delayed duopoly game with bounded rationality,” Math. Comput. Model., vol. 52, no. 9–10, pp. 1479–1489, Nov. 2010, doi: 10.1016/J.MCM.2010.06.011.
A. A. Elsadany, “Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization,” Appl. Math. Comput., vol. 294, pp. 253–263, Feb. 2017, doi: 10.1016/J.AMC.2016.09.018.
L. Fanti, “The dynamics of a banking duopoly with capital regulations,” Econ. Model., vol. 37, pp. 340–349, Feb. 2014, doi: 10.1016/J.ECONMOD.2013.11.010.
M. F. Ansori, N. Sumarti, K. A. Sidarto, and I. Gunadi, “Analyzing a macroprudential instrument during the COVID-19 pandemic using border collision bifurcation,” Rev. Electrónica Comun. y Trab. ASEPUMA Rect@, vol. 22, no. 2, pp. 113–125, 2021, doi: 10.24309/recta.2021.22.2.04.
M. F. Ansori, “Model matematik dan aplikasinya untuk menganalisis instrumen makroprudensial,” Institut Teknologi Bandung, 2021.
G.-I. Bischi, C. Chiarella, M. Kopel, and F. Szidarovszky, Nonlinear Oligopolies: Stability and Bifurcations. Berlin: Springer-Verlag, 2010.
M. A. Klein, “A theory of the banking firm,” J. Money. Credit. Bank., vol. 3, pp. 205–218, 1971.
M. Monti, “Deposit, credit and interest rates determination under alternative objective functions,” in Mathematical methods in investment and finance, G.P. Szego and K. Shell, Ed. Amsterdam, 1972.
K. Alligood, T. Sauer, and J. Yorke, Chaos: An Introduction to Dynamical Systems. New York: Springer-Verlag, 1996.
G. Gandolfo, Economic Dynamics: Methods and Models, 2nd ed. Amsterdam: Elsevier Science Publisher BV, 1985.
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,” Comput. Res. Model., vol. 13, no. 6, pp. 1275–1289, 2021, doi: 10.20537/2076-7633-2021-13-6-1275-1289.
I. Gunadi and C. A. Harun, “Revitalising reserve requirement in banking model: An industrial organisation approach,” SEACEN Occas. Pap., no. 51, 2011.
M. F. Ansori, K. A. Sidarto, and N. Sumarti, “Model of deposit and loan of a bank using spiral optimization algorithm,” J. Indones. Math. Soc., vol. 25, no. 3, pp. 292–301, 2019.
M. F. Ansori, K. A. Sidarto, and N. Sumarti, “Logistic models of deposit and loan between two banks with saving and debt transfer factors,” in AIP Conference Proceedings, 2019, vol. 2192, doi: 10.1063/1.5139148.
Copyright (c) 2022 Moch. Fandi Ansori, Susilo Hariyanto
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors who publish with this Journal agree to the following terms:
- Author retain copyright and grant the journal right of first publication with the work simultaneously licensed under a creative commons attribution license that allow others to share the work within an acknowledgement of the work’s authorship and initial publication of this journal.
- Authors are able to enter into separate, additional contractual arrangement for the non-exclusive distribution of the journal’s published version of the work (e.g. acknowledgement of its initial publication in this journal).
- Authors are permitted and encouraged to post their work online (e.g. in institutional repositories or on their websites) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published works.
1.gif)
