A Statistical Mechanics Sampling of Financial Networks Under Bilateral Netting Constraints

Abstract

We propose a statistical mechanics approach to the problem of financial network reconstruction and systemic risk when participants benefit from bilateral netting agreements. We apply physical reasoning to directly estimate individual financial liabilities from data on both total gross and net positions of total liabilities and total assets. We map this constrained network reconstruction problem to an energy-minimization one, to which we apply a Markov Chain Monte Carlo algorithmic to sample from this restricted space. These samples are then used to evaluate the impact of bilateral netting strategies to individual defaults and contagion. As an application, we employ this method to derivative networks and derive individual probabilities of default of banks. The comparison against popular alternative methods underlines the importance of restricting sample solutions to those compatible with the netting strategies of banks. We also provide an R package implementing our methodology.

Keywords: network reconstruction; financial contagion; systemic risk, bank failure, MCMC, Gibbs-Boltzmann distribution