0$, with $n$ denoting the number of banks. Furthermore, we show that this situation is rather difficult to avoid from a financial regulator's perspective: the same hardness results also hold if we apply strong restrictions on the weights of the debts, the structure of the network, or the amount of funds that banks must possess. However, if we restrict both the network structure and the amount of funds simultaneously, then the solution becomes unique, and it can be found efficiently."> 0$, with $n$ denoting the number of banks. Furthermore, we show that this situation is rather difficult to avoid from a financial regulator's perspective: the same hardness results also hold if we apply strong restrictions on the weights of the debts, the structure of the network, or the amount of funds that banks must possess. However, if we restrict both the network structure and the amount of funds simultaneously, then the solution becomes unique, and it can be found efficiently.">
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Default Ambiguity: Finding the Best Solution to the Clearing Problem

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  • P'al Andr'as Papp
  • Roger Wattenhofer
Abstract
We study financial networks with debt contracts and credit default swaps between specific pairs of banks. Given such a financial system, we want to decide which of the banks are in default, and how much of their liabilities can these defaulting banks pay. There can easily be multiple different solutions to this problem, leading to a situation of default ambiguity, and a range of possible solutions to implement for a financial authority. In this paper, we study the properties of the solution space of such financial systems, and analyze a wide range of reasonable objective functions for selecting from the set of solutions. Examples of such objective functions include minimizing the number of defaulting banks, minimizing the amount of unpaid debt, maximizing the number of satisfied banks, and many others. We show that for all of these objectives, it is NP-hard to approximate the optimal solution to an $n^{1-\epsilon}$ factor for any $\epsilon>0$, with $n$ denoting the number of banks. Furthermore, we show that this situation is rather difficult to avoid from a financial regulator's perspective: the same hardness results also hold if we apply strong restrictions on the weights of the debts, the structure of the network, or the amount of funds that banks must possess. However, if we restrict both the network structure and the amount of funds simultaneously, then the solution becomes unique, and it can be found efficiently.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2002.07741
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    References listed on IDEAS

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    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. D’Errico, Marco & Battiston, Stefano & Peltonen, Tuomas & Scheicher, Martin, 2018. "How does risk flow in the credit default swap market?," Journal of Financial Stability, Elsevier, vol. 35(C), pages 53-74.
    3. 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.
    4. Loon, Yee Cheng & Zhong, Zhaodong Ken, 2014. "The impact of central clearing on counterparty risk, liquidity, and trading: Evidence from the credit default swap market," Journal of Financial Economics, Elsevier, vol. 112(1), pages 91-115.
    5. Brett Hemenway & Sanjeev Khanna, 2015. "Sensitivity and Computational Complexity in Financial Networks," Papers 1503.07676, arXiv.org, revised Oct 2016.
    6. Hemenway, Brett & Khanna, Sanjeev, 2016. "Sensitivity and computational complexity in financial networks," Algorithmic Finance, IOS Press, vol. 5(3-4), pages 95-110.
    7. Matt V. Leduc & Sebastian Poledna & Stefan Thurner, 2016. "Systemic Risk Management in Financial Networks with Credit Default Swaps," Papers 1601.02156, arXiv.org, revised Oct 2017.
    8. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    9. 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.
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    Cited by:

    1. P'al Andr'as Papp & Roger Wattenhofer, 2021. "Debt Swapping for Risk Mitigation in Financial Networks," Papers 2107.05359, arXiv.org.
    2. P'al Andr'as Papp & Roger Wattenhofer, 2020. "Sequential Defaulting in Financial Networks," Papers 2011.10485, arXiv.org.
    3. Beni Egressy & Roger Wattenhofer, 2021. "Bailouts in Financial Networks," Papers 2106.12315, arXiv.org.

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