6 research outputs found
Finding Clearing Payments in Financial Networks with Credit Default Swaps is PPAD-complete
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
Sequential Defaulting in Financial Networks
We consider financial networks, where banks are connected by contracts such
as debts or credit default swaps. We study the clearing problem in these
systems: we want to know which banks end up in a default, and what portion of
their liabilities can these defaulting banks fulfill. We analyze these networks
in a sequential model where banks announce their default one at a time, and the
system evolves in a step-by-step manner.
We first consider the reversible model of these systems, where banks may
return from a default. We show that the stabilization time in this model can
heavily depend on the ordering of announcements. However, we also show that
there are systems where for any choice of ordering, the process lasts for an
exponential number of steps before an eventual stabilization. We also show that
finding the ordering with the smallest (or largest) number of banks ending up
in default is an NP-hard problem. Furthermore, we prove that defaulting early
can be an advantageous strategy for banks in some cases, and in general,
finding the best time for a default announcement is NP-hard. Finally, we
discuss how changing some properties of this setting affects the stabilization
time of the process, and then use these techniques to devise a monotone model
of the systems, which ensures that every network stabilizes eventually