Financial Networks with Singleton Liability Priorities

Stavros D. Ioannidis, Bart de Keijzer, Carmine Ventre

Abstract: Financial networks model debt obligations between economic firms. Computational and game-theoretic analyses of these networks have been recent focus of the literature. The main computational challenge in this context is the clearing problem, a fixed point search problem that essentially determines insolvent firms and their exposure to systemic risk, technically known as recovery rates. When Credit Default Swaps, a derivative connected to the 2008 financial crisis, are part of the obligations and insolvent firms pay the same proportion of all their debts, computing a weakly approximate solution is $$\textsf {PPAD}$$ -complete [29], whereas computing a strongly approximate solution is $$\textsf {FIXP}$$ -complete [17]. This paper addresses the computational complexity of the clearing problem in financial networks with derivatives, whenever priorities amongst creditors are adopted. This practically relevant model has been only studied from a game-theoretic standpoint. We explicitly study the clearing problem whenever the firms pay according to a singleton liability priority list and prove that it is FIXP-complete. Finally, we provide a host of $$\textsf {NP}$$ -hardness results for the computation of priority lists that optimise specific objectives of importance in the domain.