The Computational Complexity of Clearing Financial Networks with Credit Default Swaps.

We consider the problem of clearing a system of interconnected banks. Prior work has shown 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 work, we show that the computational complexity of the clearing problem drastically increases when banks can also enter into credit default swaps (CDSs), i.e., financial derivative contracts that depend on the default of another bank. We first show that many important decision problems are NP-hard once CDSs are allowed. This includes deciding if a specific bank is at risk of default and deciding if a clearing vector exists in the first place. Second, we show that computing an approximate solution to the clearing problem with sufficiently small constant error is PPAD-complete. To prove our results, we demonstrate how financial networks with debt and CDSs can encode Boolean and arithmetic operations. Our results have practical importance for network stress tests and they reveal computational complexity as a new concern regarding the stability of the financial system.