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Finding Clearing Payments in Financial Networks with Credit Default Swaps is PPAD-complete


Schuldenzucker, Steffen; Seuken, Sven; Battiston, Stefano (2017). Finding Clearing Payments in Financial Networks with Credit Default Swaps is PPAD-complete. In: The 8th Innovations in Theoretical Computer Science (ITCS) Conference, Berkeley, 9 January 2017 - 11 January 2017.

Abstract

We consider the problem of clearing a system of interconnected banks that have been exposed to a shock on their assets. Eisenberg and Noe (2001) showed that when banks can only enter into simple debt contracts with each other, then a clearing vector of payments can be computed in polynomial time. In this paper, we show that the situation changes radically when banks can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank. We prove that computing an approximate solution to the clearing problem with sufficiently small constant error is PPAD-complete. To do this, we demonstrate how financial networks with debt and CDSs can encode arithmetic operations such as addition and multiplication. Our results have practical impact for network stress tests and reveal computational complexity as a new concern regarding the stability of the financial system.

Abstract

We consider the problem of clearing a system of interconnected banks that have been exposed to a shock on their assets. Eisenberg and Noe (2001) showed that when banks can only enter into simple debt contracts with each other, then a clearing vector of payments can be computed in polynomial time. In this paper, we show that the situation changes radically when banks can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank. We prove that computing an approximate solution to the clearing problem with sufficiently small constant error is PPAD-complete. To do this, we demonstrate how financial networks with debt and CDSs can encode arithmetic operations such as addition and multiplication. Our results have practical impact for network stress tests and reveal computational complexity as a new concern regarding the stability of the financial system.

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Additional indexing

Item Type:Conference or Workshop Item (Paper), not refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Informatics
Dewey Decimal Classification:000 Computer science, knowledge & systems
Event End Date:11 January 2017
Deposited On:20 Feb 2018 17:16
Last Modified:14 Mar 2018 18:04
Publisher:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
Series Name:LIPIcs : Leibniz International Proceedings in Informatics
Number:67
ISSN:1868-8969
ISBN:978-3-95977-029-3
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.4230/LIPIcs.ITCS.2017.32
Related URLs:http://drops.dagstuhl.de/opus/volltexte/2017/8155 (Publisher)
Other Identification Number:merlin-id:14567

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