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Improved Hardness Results for the Clearing Problem in Financial Networks with Credit Default Swaps

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  • Simon Dohn
  • Kristoffer Arnsfelt Hansen
  • Asger Klinkby

Abstract

We study computational problems in financial networks of banks connected by debt contracts and credit default swaps (CDSs). A main problem is to determine \emph{clearing} payments, for instance right after some banks have been exposed to a financial shock. Previous works have shown the $\varepsilon$-approximate version of the problem to be $\mathrm{PPAD}$-complete and the exact problem $\mathrm{FIXP}$-complete. We show that $\mathrm{PPAD}$-hardness hold when $\varepsilon \approx 0.101$, improving the previously best bound significantly. Due to the fact that the clearing problem typically does not have a unique solution, or that it may not have a solution at all in the presence of default costs, several natural decision problems are also of great interest. We show two such problems to be $\exists\mathbb{R}$-complete, complementing previous $\mathrm{NP}$-hardness results for the approximate setting.

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  • Simon Dohn & Kristoffer Arnsfelt Hansen & Asger Klinkby, 2024. "Improved Hardness Results for the Clearing Problem in Financial Networks with Credit Default Swaps," Papers 2409.18717, arXiv.org.
    • Handle: RePEc:arx:papers:2409.18717
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    References listed on IDEAS

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    1. Steffen Schuldenzucker & Sven Seuken & Stefano Battiston, 2017. "The Computational Complexity of Financial Networks with Credit Default Swaps," Papers 1710.01578, arXiv.org, revised May 2019.
    2. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
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