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Sensitivity and Computational Complexity in Financial Networks

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  • Brett Hemenway
  • Sanjeev Khanna

Abstract

Modern financial networks exhibit a high degree of interconnectedness and determining the causes of instability and contagion in financial networks is necessary to inform policy and avoid future financial collapse. In the American Economic Review, Elliott, Golub and Jackson proposed a simple model for capturing the dynamics of complex financial networks. In Elliott, Golub and Jackson's model, each institution in the network can buy underlying assets or percentage shares in other institutions (cross-holdings) and if any institution's value drops below a critical threshold value, its value suffers an additional failure cost. This work shows that even in simple model put forward by Elliott, Golub and Jackson there are fundamental barriers to understanding the risks that are inherent in a network. First, if institutions are not required to maintain a minimum amount of self-holdings, an $\epsilon$ change in investments by a single institution can have an arbitrarily magnified influence on the net worth of the institutions in the system. This sensitivity result shows that if institutions have small self-holdings, then estimating the market value of an institution requires almost perfect information about every cross-holding in the system. Second, we show that even if a regulator has complete information about all cross-holdings in the system, it may be computationally intractable to even estimate the number of failures that could be caused by an arbitrarily small shock to the system. Together, these results show that any uncertainty in the cross-holdings or values of the underlying assets can be amplified by the network to arbitrarily large uncertainty in the valuations of institutions in the network.

Suggested Citation

  • Brett Hemenway & Sanjeev Khanna, 2015. "Sensitivity and Computational Complexity in Financial Networks," Papers 1503.07676, arXiv.org, revised Oct 2016.
  • Handle: RePEc:arx:papers:1503.07676
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    References listed on IDEAS

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    1. Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
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    Cited by:

    1. P'al Andr'as Papp & Roger Wattenhofer, 2020. "Default Ambiguity: Finding the Best Solution to the Clearing Problem," Papers 2002.07741, arXiv.org, revised Oct 2021.
    2. Nils Bertschinger & Martin Hoefer & Daniel Schmand, 2019. "Flow Allocation Games," Papers 1908.01714, arXiv.org, revised Dec 2023.
    3. Dylan Herman & Cody Googin & Xiaoyuan Liu & Alexey Galda & Ilya Safro & Yue Sun & Marco Pistoia & Yuri Alexeev, 2022. "A Survey of Quantum Computing for Finance," Papers 2201.02773, arXiv.org, revised Jun 2022.
    4. Beni Egressy & Roger Wattenhofer, 2021. "Bailouts in Financial Networks," Papers 2106.12315, arXiv.org.

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