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Centralized Clearing Mechanisms in Financial Networks: A Programming Approach

Author

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  • Péter Csóka

    (Department of Finance, Corvinus University of Budapest and Centre for Economic and Regional Studies)

  • P. Jean-Jacques Herings

    (Department of Econometrics and Operations Research, Tilburg University)

Abstract

We consider financial networks where agents are linked to each other with financial contracts. A centralized clearing mechanism collects the initial endowments, the liabilities and the division rules of the agents and determines the payments to be made. A division rule specifies how the assets of the agents should be rationed, the four most common ones being the proportional, the priority, the constrained equal awards, and the constrained equal losses division rules. Since payments made depend on payments received, we are looking for solutions to a system of equations. The set of solutions is known to have a lattice structure, leading to the existence of a least and a greatest clearing payment matrix. Previous research has shown how decentralized clearing selects the least clearing payment matrix. We present a centralized approach towards clearing in order to select the greatest clearing payment matrix. To do so, we formulate the determination of the greatest clearing payment matrix as a programming problem. When agents use proportional division rules, this programming problem corresponds to a linear programming problem. We show that for the other common division rules, it can be written as an integer linear programming problem.

Suggested Citation

  • Péter Csóka & P. Jean-Jacques Herings, 2022. "Centralized Clearing Mechanisms in Financial Networks: A Programming Approach," CERS-IE WORKING PAPERS 2208, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:2208
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    References listed on IDEAS

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    1. Gabrielle Demange, 2018. "Contagion in Financial Networks: A Threat Index," Management Science, INFORMS, vol. 64(2), pages 955-970, February.
    2. Péter Csóka & P. Jean-Jacques Herings, 2021. "Uniqueness of Clearing Payment Matrices in Financial Networks," CERS-IE WORKING PAPERS 2134, Institute of Economics, Centre for Economic and Regional Studies.
    3. Flores-Szwagrzak, Karol, 2015. "Priority classes and weighted constrained equal awards rules for the claims problem," Journal of Economic Theory, Elsevier, vol. 160(C), pages 36-55.
    4. Martijn W. Ketelaars & Peter Borm, 2024. "On the unification of centralized and decentralized clearing mechanisms in financial networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(3), pages 205-231, June.
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    Cited by:

    1. Ketelaars, Martijn, 2024. "Clearing in financial networks and dynamic investment under uncertainty," Other publications TiSEM 94768fb9-fd72-405d-a330-6, Tilburg University, School of Economics and Management.
    2. Martijn W. Ketelaars & Peter Borm, 2024. "On the unification of centralized and decentralized clearing mechanisms in financial networks," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 99(3), pages 205-231, June.
    3. Ketelaars, Martijn & Borm, Peter & Herings, P.J.J., 2024. "The Characterization of Clearing Payments in Financial Networks," Other publications TiSEM e1e1e64f-022b-4206-b7b3-b, Tilburg University, School of Economics and Management.
    4. Mih'aly P'eter Hanics, 2022. "Graph theoretical models and algorithms of portfolio compression," Papers 2212.09473, arXiv.org.

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    More about this item

    Keywords

    Financial networks; systemic risk; bankruptcy rules; clearing; integer linear programming;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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