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Systemic Risk and Interbank Lending

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  • Li-Hsien Sun

    (National Central University)

Abstract

We propose a simple model of the banking system incorporating a game feature, where the evolution of monetary reserve is modeled as a system of coupled Feller diffusions. The optimization reflects the desire of each bank to borrow from or lend to a central bank through manipulating its lending preference and the intention of each bank to deposit in the central bank in order to control the reserve and the corresponding volatility for cost minimization. The Markov Nash equilibrium for finite many players generated by minimizing the linear quadratic cost subject to Cox–Ingersoll–Ross type processes creates liquidity and deposit rate. The adding liquidity leads to a flocking effect implying stability or systemic risk depending on the level of the growth rate, but the deposit rate diminishes the growth of the total monetary reserve causing a large number of bank defaults. The central bank acts as a central deposit corporation. In addition, the corresponding mean field game in the case of the number of banks N large and the infinite time horizon stochastic game with the discount factor are also discussed.

Suggested Citation

  • Li-Hsien Sun, 2018. "Systemic Risk and Interbank Lending," Journal of Optimization Theory and Applications, Springer, vol. 179(2), pages 400-424, November.
    • Handle: RePEc:spr:joptap:v:179:y:2018:i:2:d:10.1007_s10957-017-1185-1
    DOI: 10.1007/s10957-017-1185-1
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    References listed on IDEAS

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    1. A. Bensoussan & K. C. J. Sung & S. C. P. Yam & S. P. Yung, 2016. "Linear-Quadratic Mean Field Games," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 496-529, May.
    2. Gilles-Edouard Espinosa & Nizar Touzi, 2015. "Optimal Investment Under Relative Performance Concerns," Mathematical Finance, Wiley Blackwell, vol. 25(2), pages 221-257, April.
    3. Rene Carmona & Jean-Pierre Fouque & Seyyed Mostafa Mousavi & Li-Hsien Sun, 2016. "Systemic Risk and Stochastic Games with Delay," Papers 1607.06373, arXiv.org.
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    Cited by:

    1. Zachary Feinstein & Andreas Sojmark, 2019. "A Dynamic Default Contagion Model: From Eisenberg-Noe to the Mean Field," Papers 1912.08695, arXiv.org.
    2. Rama Cont & Xin Guo & Renyuan Xu, 2020. "Pareto Optima for a Class of Singular Control Games," Working Papers hal-03049246, HAL.
    3. Lorella Fatone & Francesca Mariani, 2020. "Systemic risk governance in a dynamical model of a banking system with stochastic assets and liabilities," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 15(1), pages 183-219, January.
    4. Tomoyuki Ichiba & Michael Ludkovski & Andrey Sarantsev, 2019. "Dynamic contagion in a banking system with births and defaults," Annals of Finance, Springer, vol. 15(4), pages 489-538, December.
    5. Lijun Bo & Tongqing Li & Xiang Yu, 2021. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Papers 2106.09978, arXiv.org, revised May 2022.
    6. Tabak, Benjamin Miranda & Silva, Thiago Christiano & Fiche, Marcelo Estrela & Braz, Tércio, 2021. "Citation likelihood analysis of the interbank financial networks literature: A machine learning and bibliometric approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    7. Aditya Maheshwari & Andrey Sarantsev, 2018. "Modeling Financial System with Interbank Flows, Borrowing, and Investing," Risks, MDPI, vol. 6(4), pages 1-26, November.
    8. Doumpos, Michalis & Zopounidis, Constantin & Gounopoulos, Dimitrios & Platanakis, Emmanouil & Zhang, Wenke, 2023. "Operational research and artificial intelligence methods in banking," European Journal of Operational Research, Elsevier, vol. 306(1), pages 1-16.
    9. Chotipong Charoensom & Thaisiri Watewai, 2022. "Optimal Liquidity Control and Systemic Risk in an Interbank Network with Liquidity Shocks and Regime-dependent Interconnectedness," PIER Discussion Papers 175, Puey Ungphakorn Institute for Economic Research.
    10. Rama Cont & Xin Guo & Renyuan Xu, 2021. "Interbank lending with benchmark rates: Pareto optima for a class of singular control games," Mathematical Finance, Wiley Blackwell, vol. 31(4), pages 1357-1393, October.
    11. Li-Hsien Sun, 2022. "Mean Field Games with Heterogeneous Groups: Application to Banking Systems," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 130-167, January.
    12. Bo, Lijun & Li, Tongqing & Yu, Xiang, 2022. "Centralized systemic risk control in the interbank system: Weak formulation and Gamma-convergence," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 622-654.
    13. Yu-Jui Huang & Li-Hsien Sun, 2023. "Partial Information Breeds Systemic Risk," Papers 2312.04045, arXiv.org, revised Dec 2023.

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