How is Systemic Risk Amplified by Three Typical Financial Networks

Financial institutions are typically tied together via inter-liability, portfolio overlapping and share cross-holding. These connections among financial institutions constitute the three most common financial networks, which may lead to financial risk contagion and even systemic risk when some institutions suffer shock. In this paper, firstly, for a given shock, we prove the existence of the equilibrium clearing vector of the financial system characterized by these three typical financial networks. Then, we mathematically derive an analytical form to show how these three contagion channels jointly affect and amplify the loss of the non-default institutions, and explain how the lack of liquidity of external investment assets exacerbates the loss caused by portfolio overlapping. Finally, the influence of the characteristics of financial network on risk contagion is verified by numerical simulation. These results provide basis for understanding the financial systemic risk contagion in the real world.