Linearities, Non-Linearities and Phase Transitions in Loss Diffusion Processes in Financial Networks

Banks and financial institutions are linked by financial obligations that form complex networks. These networks serve risk-sharing purposes and become channels of contagion in the event of liquidity and insolvency shocks. The consequent processes of loss diffusion are usually non-linear and, in some cases, exhibit phase transitions from situations in which there is no default contagion to a systemic crisis that involves the entire network. In this paper, I discuss the results of recent numerical simulations of contagion processes in financial networks that present some unexpected linearities