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Using Shapley’s asymmetric power index to measure banks’ contributions to systemic risk

Author

Listed:
  • Rodney Garratt

    (University of California, Santa Barbara)

  • Lewis Webber

    (Bank of England)

  • Matthew Willison

    (Bank of England)

Abstract

An individual bank can put the whole banking system at risk if its losses in response to shocks push losses for the system as a whole above a critical threshold. We determine the contribution of banks to this systemic risk using a generalisation of the Shapley value; a concept originating in co-operative game theory. An important feature of this approach is that the order in which banks fail in response to a shock depends on the composition of the banks’ asset portfolios and capital buffers. We show how these factors affect banks’ contributions to systemic risk, and the extent to which these contributions depend on the level of the critical threshold.

Suggested Citation

  • Rodney Garratt & Lewis Webber & Matthew Willison, 2012. "Using Shapley’s asymmetric power index to measure banks’ contributions to systemic risk," Bank of England working papers 468, Bank of England.
  • Handle: RePEc:boe:boeewp:0468
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    References listed on IDEAS

    as
    1. Gauthier, Céline & Lehar, Alfred & Souissi, Moez, 2012. "Macroprudential capital requirements and systemic risk," Journal of Financial Intermediation, Elsevier, vol. 21(4), pages 594-618.
    2. Roth, Ae & Verrecchia, Re, 1979. "Shapley Value As Applied To Cost Allocation - Reinterpretation," Journal of Accounting Research, Wiley Blackwell, vol. 17(1), pages 295-303.
    3. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    4. Lewis Webber & Matthew Willison, 2011. "Systemic capital requirements," Bank of England working papers 436, Bank of England.
    5. Shapley, L. S. & Shubik, Martin, 1954. "A Method for Evaluating the Distribution of Power in a Committee System," American Political Science Review, Cambridge University Press, vol. 48(3), pages 787-792, September.
    6. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
    7. Lewis Webber & Matthew Willison, 2011. "Systemic capital requirements," BIS Papers chapters, in: Bank for International Settlements (ed.), Macroprudential regulation and policy, volume 60, pages 44-50, Bank for International Settlements.
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    Cited by:

    1. Fuad Aleskerov & Irina Andrievskaya & Elena Permjakova, 2014. "Key Borrowers Detected By The Intensities Of Their Short-range Interactions," HSE Working papers WP BRP 33/FE/2014, National Research University Higher School of Economics.

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    More about this item

    Keywords

    Shapley value; systemic risk; bank regulation;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • G01 - Financial Economics - - General - - - Financial Crises
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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