This paper takes a financial network, applies a shock to the system and looks at the resulting institutions that fail. It considers the propagation of contagion through the financial network by employing various techniques. The first method calculates unique clearing payments for all the banks in the system. It also defines fundamental default and contagious failure of any financial institution and differentiates between these two important concepts.
The second method uses mean-field approximations to make all the banks in the system identical. It reduces an institution's external assets so that it defaults and looks at subsequent failures that spread through the financial network. This technique provides criteria for shocks and for initial and successive defaults. It considers cases with and without liquidity shocks.
This paper presents a connectivity measure using Kirchhoff's theorem. It computes the Kirchhoff number of all the banks in a financial network and finds the most and least vulnerable institutions. Finally, this paper tests the described connectivity measure by performing simulations on financial systems with a varying number of large banks and analyzing the results
