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Dynamic contagion in a banking system with births and defaults

Author

Listed:
  • Tomoyuki Ichiba

    (University of California)

  • Michael Ludkovski

    (University of California)

  • Andrey Sarantsev

    (University of Nevada)

Abstract

We consider a dynamic model of interconnected banks. New banks can emerge, and existing banks can default, creating a birth-and-death setup. Microscopically, banks evolve as independent geometric Brownian motions. Systemic effects are captured through default contagion: as one bank defaults, reserves of other banks are reduced by a random proportion. After examining the long-term stability of this system, we investigate mean-field limits as the number of banks tends to infinity. Our main results concern the measure-valued scaling limit which is governed by a McKean–Vlasov jump-diffusion. The default impact creates a mean-field drift, while the births and defaults introduce jump terms tied to the current distribution of the process. Individual dynamics in the limit is described by the propagation of chaos phenomenon. In certain cases, we explicitly characterize the limiting average reserves.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:annfin:v:15:y:2019:i:4:d:10.1007_s10436-019-00351-2
    DOI: 10.1007/s10436-019-00351-2
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    References listed on IDEAS

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    3. Alexander Lipton & Vadim Kaushansky & Christoph Reisinger, 2018. "Semi-analytical solution of a McKean-Vlasov equation with feedback through hitting a boundary," Papers 1808.05311, arXiv.org, revised Aug 2018.
    4. Graham, Carl, 1992. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 69-82, February.
    5. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
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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.

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    More about this item

    Keywords

    Default contagion; Mean field limit; Interacting birth-and-death process; McKean–Vlasov jump-diffusion; Propagation of chaos; Lyapunov function;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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