IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v30y2020i4p1181-1204.html
   My bibliography  Save this article

Network valuation in financial systems

Author

Listed:
  • Paolo Barucca
  • Marco Bardoscia
  • Fabio Caccioli
  • Marco D'Errico
  • Gabriele Visentin
  • Guido Caldarelli
  • Stefano Battiston

Abstract

We introduce a general model for the balance‐sheet consistent valuation of interbank claims within an interconnected financial system. Our model represents an extension of clearing models of interdependent liabilities to account for the presence of uncertainty on banks' external assets. At the same time, it also provides a natural extension of classic structural credit risk models to the case of an interconnected system. We characterize the existence and uniqueness of a valuation that maximizes individual and total equity values for all banks. We apply our model to the assessment of systemic risk and in particular for the case of stress testing. Further, we provide a fixed‐point algorithm to carry out the network valuation and the conditions for its convergence.

Suggested Citation

  • Paolo Barucca & Marco Bardoscia & Fabio Caccioli & Marco D'Errico & Gabriele Visentin & Guido Caldarelli & Stefano Battiston, 2020. "Network valuation in financial systems," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1181-1204, October.
  • Handle: RePEc:bla:mathfi:v:30:y:2020:i:4:p:1181-1204
    DOI: 10.1111/mafi.12272
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/mafi.12272
    Download Restriction: no

    File URL: https://libkey.io/10.1111/mafi.12272?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Marco Bardoscia & Stefano Battiston & Fabio Caccioli & Guido Caldarelli, 2016. "Pathways towards instability in financial networks," Papers 1602.05883, arXiv.org, revised Feb 2017.
    2. Marco Bardoscia & Stefano Battiston & Fabio Caccioli & Guido Caldarelli, 2015. "DebtRank: A Microscopic Foundation for Shock Propagation," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-13, June.
    3. Leland, Hayne E & Toft, Klaus Bjerre, 1996. "Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    4. Caccioli, Fabio & Shrestha, Munik & Moore, Cristopher & Farmer, J. Doyne, 2014. "Stability analysis of financial contagion due to overlapping portfolios," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 233-245.
    5. Daron Acemoglu & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2015. "Systemic Risk and Stability in Financial Networks," American Economic Review, American Economic Association, vol. 105(2), pages 564-608, February.
    6. Zachary Feinstein & Weijie Pang & Birgit Rudloff & Eric Schaanning & Stephan Sturm & Mackenzie Wildman, 2017. "Sensitivity of the Eisenberg-Noe clearing vector to individual interbank liabilities," Papers 1708.01561, arXiv.org, revised Oct 2018.
    7. Franklin Allen & Elena Carletti, 2013. "What Is Systemic Risk?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45, pages 121-127, August.
    8. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    9. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    10. Freixas, Xavier & Parigi, Bruno M & Rochet, Jean-Charles, 2000. "Systemic Risk, Interbank Relations, and Liquidity Provision by the Central Bank," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(3), pages 611-638, August.
    11. Tiziano Squartini & Guido Caldarelli & Giulio Cimini & Andrea Gabrielli & Diego Garlaschelli, 2018. "Reconstruction methods for networks: the case of economic and financial systems," Papers 1806.06941, arXiv.org.
    12. Helmut Elsinger & Alfred Lehar & Martin Summer, 2006. "Risk Assessment for Banking Systems," Management Science, INFORMS, vol. 52(9), pages 1301-1314, September.
    13. Joseph E. Stiglitz, 2010. "Risk and Global Economic Architecture: Why Full Financial Integration May Be Undesirable," American Economic Review, American Economic Association, vol. 100(2), pages 388-392, May.
    14. Glasserman, Paul & Young, H. Peyton, 2016. "Contagion in financial networks," LSE Research Online Documents on Economics 68681, London School of Economics and Political Science, LSE Library.
    15. Matthew Elliott & Benjamin Golub & Matthew O. Jackson, 2014. "Financial Networks and Contagion," American Economic Review, American Economic Association, vol. 104(10), pages 3115-3153, October.
    16. Hamed Amini & Rama Cont & Andreea Minca, 2016. "Resilience To Contagion In Financial Networks," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 329-365, April.
    17. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    18. Rama Cont & Eric Schaanning, 2017. "Fire sales, indirect contagion and systemic stress testing," Working Paper 2017/2, Norges Bank.
    19. Franklin Allen & Elena Carletti, 2013. "What Is Systemic Risk?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(s1), pages 121-127, August.
    20. Jean-Charles Rochet & Jean Tirole, 1996. "Interbank lending and systemic risk," Proceedings, Board of Governors of the Federal Reserve System (U.S.), pages 733-765.
    21. Kartik Anand & Ben Craig & Goetz von Peter, 2015. "Filling in the blanks: network structure and interbank contagion," Quantitative Finance, Taylor & Francis Journals, vol. 15(4), pages 625-636, April.
    22. Preis, Tobias & Bardoscia, Marco & Caccioli, Fabio & Perotti, Juan Ignacio & Vivaldo, Gianna & Caldarelli, Guido, 2016. "Distress propagation in complex networks: the case of non-linear DebtRank," LSE Research Online Documents on Economics 68598, London School of Economics and Political Science, LSE Library.
    23. Battiston Stefano & Caldarelli Guido & D’Errico Marco & Gurciullo Stefano, 2016. "Leveraging the network: A stress-test framework based on DebtRank," Statistics & Risk Modeling, De Gruyter, vol. 33(3-4), pages 117-138, December.
    24. Paul Glasserman & H. Peyton Young, 2016. "Contagion in Financial Networks," Journal of Economic Literature, American Economic Association, vol. 54(3), pages 779-831, September.
    25. Furfine, Craig H, 2003. "Interbank Exposures: Quantifying the Risk of Contagion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(1), pages 111-128, February.
    26. Glasserman, Paul & Young, H. Peyton, 2015. "How likely is contagion in financial networks?," Journal of Banking & Finance, Elsevier, vol. 50(C), pages 383-399.
    27. Olga Lewandowska, 2015. "OTC Clearing Arrangements for Bank Systemic Risk Regulation: A Simulation Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 47(6), pages 1177-1203, September.
    28. L. C. G. Rogers & L. A. M. Veraart, 2013. "Failure and Rescue in an Interbank Network," Management Science, INFORMS, vol. 59(4), pages 882-898, April.
    29. Tom Fischer, 2014. "No-Arbitrage Pricing Under Systemic Risk: Accounting For Cross-Ownership," Mathematical Finance, Wiley Blackwell, vol. 24(1), pages 97-124, January.
    30. Didier Cossin & Henry Schellhorn, 2007. "Credit Risk in a Network Economy," Management Science, INFORMS, vol. 53(10), pages 1604-1617, October.
    31. Rodrigo Cifuentes & Hyun Song Shin & Gianluigi Ferrucci, 2005. "Liquidity Risk and Contagion," Journal of the European Economic Association, MIT Press, vol. 3(2-3), pages 556-566, 04/05.
    32. Johannes Hain & Tom Fischer, 2015. "Valuation Algorithms for Structural Models of Financial Interconnectedness," Papers 1501.07402, arXiv.org.
    33. Helmut Elsinger & Alfred Lehar & Martin Summer, 2006. "Using Market Information for Banking System Risk Assessment," International Journal of Central Banking, International Journal of Central Banking, vol. 2(1), March.
    34. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    35. Marco Bardoscia & Fabio Caccioli & Juan Ignacio Perotti & Gianna Vivaldo & Guido Caldarelli, 2016. "Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-12, October.
    36. Giulio Cimini & Tiziano Squartini & Diego Garlaschelli & Andrea Gabrielli, 2014. "Systemic risk analysis in reconstructed economic and financial networks," Papers 1411.7613, arXiv.org, revised May 2015.
    37. Marco Bardoscia & Fabio Caccioli & Juan Ignacio Perotti & Gianna Vivaldo & Guido Caldarelli, 2015. "Distress propagation in complex networks: the case of non-linear DebtRank," Papers 1512.04460, arXiv.org, revised Sep 2016.
    38. Paul Glasserman & Peyton Young, 2015. "Contagion in Financial Networks," Economics Series Working Papers 764, University of Oxford, Department of Economics.
    39. Marco Bardoscia & Stefano Battiston & Fabio Caccioli & Guido Caldarelli, 2017. "Pathways towards instability in financial networks," Nature Communications, Nature, vol. 8(1), pages 1-7, April.
    40. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
    41. Veraart, Luitgard A. M., 2020. "Distress and default contagion in financial networks," LSE Research Online Documents on Economics 101905, London School of Economics and Political Science, LSE Library.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marco Bardoscia & Paolo Barucca & Stefano Battiston & Fabio Caccioli & Giulio Cimini & Diego Garlaschelli & Fabio Saracco & Tiziano Squartini & Guido Caldarelli, 2021. "The Physics of Financial Networks," Papers 2103.05623, arXiv.org.
    2. Bardoscia, Marco & Barucca, Paolo & Brinley Codd, Adam & Hill, John, 2017. "The decline of solvency contagion risk," Bank of England working papers 662, Bank of England.
    3. Bardoscia, Marco & Barucca, Paolo & Codd, Adam Brinley & Hill, John, 2019. "Forward-looking solvency contagion," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    4. Carro, Adrian & Stupariu, Patricia, 2024. "Uncertainty, non-linear contagion and the credit quality channel: An application to the Spanish interbank market," Journal of Financial Stability, Elsevier, vol. 71(C).
    5. Fabio Caccioli & Paolo Barucca & Teruyoshi Kobayashi, 2018. "Network models of financial systemic risk: a review," Journal of Computational Social Science, Springer, vol. 1(1), pages 81-114, January.
    6. Spiros Bougheas & Adam Hal Spencer, 2022. "Fire sales and ex ante valuation of systemic risk: A financial equilibrium networks approach," Discussion Papers 2022/04, University of Nottingham, Centre for Finance, Credit and Macroeconomics (CFCM).
    7. Alessandro Ferracci & Giulio Cimini, 2021. "Systemic risk in interbank networks: disentangling balance sheets and network effects," Papers 2109.14360, arXiv.org, revised Sep 2022.
    8. Valentina Macchiati & Giuseppe Brandi & Tiziana Di Matteo & Daniela Paolotti & Guido Caldarelli & Giulio Cimini, 2022. "Systemic liquidity contagion in the European interbank market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(2), pages 443-474, April.
    9. Chen, Yu & Jin, Shuyue & Wang, Xiasi, 2021. "Solvency contagion risk in the Chinese commercial banks’ network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    10. Sadamori Kojaku & Giulio Cimini & Guido Caldarelli & Naoki Masuda, 2018. "Structural changes in the interbank market across the financial crisis from multiple core-periphery analysis," Papers 1802.05139, arXiv.org.
    11. Wiersema, Garbrand & Kleinnijenhuis, Alissa M. & Wetzer, Thom & Farmer, J. Doyne, 2023. "Scenario-free analysis of financial stability with interacting contagion channels," Journal of Banking & Finance, Elsevier, vol. 146(C).
    12. Yongli Li & Guanghe Liu & Paolo Pin, 2018. "Network-based risk measurements for interbank systems," PLOS ONE, Public Library of Science, vol. 13(7), pages 1-18, July.
    13. Bardoscia, Marco & Ka-Kay Pang, Raymond, 2023. "Ring-fencing in financial networks," Bank of England working papers 1046, Bank of England.
    14. Brandi, Giuseppe & Di Clemente, Riccardo & Cimini, Giulio, 2018. "Epidemics of liquidity shortages in interbank markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 255-267.
    15. Paolo Bartesaghi & Michele Benzi & Gian Paolo Clemente & Rosanna Grassi & Ernesto Estrada, 2019. "Risk-dependent centrality in economic and financial networks," Papers 1907.07908, arXiv.org, revised Apr 2020.
    16. Aikman, David & Beale, Daniel & Brinley-Codd, Adam & Covi, Giovanni & Hüser, Anne‑Caroline & Lepore, Caterina, 2023. "Macroprudential stress‑test models: a survey," Bank of England working papers 1037, Bank of England.
    17. Tiziano Squartini & Guido Caldarelli & Giulio Cimini & Andrea Gabrielli & Diego Garlaschelli, 2018. "Reconstruction methods for networks: the case of economic and financial systems," Papers 1806.06941, arXiv.org.
    18. Barnett, William A. & Wang, Xue & Xu, Hai-Chuan & Zhou, Wei-Xing, 2022. "Hierarchical contagions in the interdependent financial network," Journal of Financial Stability, Elsevier, vol. 61(C).
    19. Luitgard Anna Maria Veraart, 2020. "Distress and default contagion in financial networks," Mathematical Finance, Wiley Blackwell, vol. 30(3), pages 705-737, July.
    20. Covi, Giovanni & Gorpe, Mehmet Ziya & Kok, Christoffer, 2021. "CoMap: Mapping Contagion in the Euro Area Banking Sector," Journal of Financial Stability, Elsevier, vol. 53(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:30:y:2020:i:4:p:1181-1204. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.