Systemic risk in financial networks -- a computational perspective

11^th October 2022, 13:00 Ashton Lecture Theatre
Prof. Carmine Ventre
King`s College London

Abstract

We are given a network modelling assets and liabilities of the financial institutions in the system. We study the following basic question: Can we efficiently compute the exposure rate of each bank to defaults in the system?

The answer is yes if there are no financial derivatives (i.e., conditional obligations) in the network. When we introduce derivatives, specifically Credit Default Swaps (CDS), the problem is complete for the complexity class PPAD if one is content with "almost" (that is, weakly approximate) solutions that could grossly under- and over-estimate each bank's exposure.

What about solutions where the rate is precise to say 1%? We prove that computing these strong approximations up to any given precision is complete for the class FIXP, capturing hardness due to numerical aspects (in particular, the irrationality of the actual solution) in addition to the combinatorial issues modelled by PPAD.

We also study the relationship between the network structure and the (ir)rationality of the solution, the robustness of our findings to different payment rules of insolvent banks and the computational complexity of questions motivated by the needs of regulators. Overall, our results support a ban of the purely speculative naked CDS and uncover a connection between FIXP and efficient algorithms in the real computational model of Blum-Shub-Smale.

Talk based on joint work with Stavros Ioannidis and Bart de Keijzer.