|Source: Elliott et al. 2013|
"If there is no integration then clearly there cannot be any contagion. As integration increases, the exposure of organizations to each other increases and so contagions become possible. Thus, on a basic level increasing integration leads to increased exposure which tends to increase the probability and extent of contagions. The countervailing effect here is that an organization's dependence on its own primitive assets decreases as it becomes integrated. Thus, although integration can increase the likelihood of a cascade once an initial failure occurs, it can also decrease the likelihood of that first failure...
With low levels of diversification, organizations can be very sensitive to particular others, but the network of interdependencies is disconnected and overall cascades are limited in extent. As diversification increases, a "sweet spot" is hit where organizations have enough of their cross-holdings concentrated in particular other organizations so that a cascade can occur, and yet the network of cross-holdings is connected enough for the contagion to be far-reaching. Finally, as diversification is further increased, organizations' portfolios are sufficiently diversified so that they become insensitive to any particular organization's failure."Near the end of the paper, they illustrate the model using cross-holdings of debt among six European countries. The figure above is their representation of financial interdependencies in Europe. They conduct something akin to stress tests, simulating cascades of failures under various scenarios that very roughly approximate conditions in 2008. The simulations find that, following a first failure in Greece, Portugal is fails from contagion. After Portugal fails, Spain fails due to its large exposure to Portugal. The high exposure of France and Germany to Spain causes them to fail next in most simulations. Italy is always last to fail due to its low exposure to others' debt. They emphasize that this is intended only as an illustrative exercise at this stage, but could eventually be refined and incorporated into analysis of failure and contagion risk.
*Edited to fix my mistake pointed out by Phil.