There are three conditions required for a cascade, there are; a failure, contagion and interconnection.
[1] Diversification and integration in the financial network determine whether and how failures will spread.
Elliot, Golub and Jackson (2013) characterize the financial network by diversification and integration.
Using random network, the authors [2] show that high integration decreases the percentage of first failures; and as the network approaches complete integration the percentage of the first failures approaches zero.
However, the integration increases the percentage of organizations that fail due to higher interconnection.
In addition, up to some threshold, diversification does increase the percentage of discontinuous drops in value.
Eliot, Golub and Jackson (2013) provide an empirical method how to model cascades in financial networks.
Their model starts with the following assumptions (all notations are borrowed from Elliot, Golub and Jackson (2013)): The authors find the equity value of an organization using the works by Brioschi, Buzzachi and Colombo (1989)[4] and Fedina, Hodder and Trianitis (1994):[5] The equity value is defined as the value of primitive assets and the value of claims on the primitive assets in other organizations in the network.
The counterpart of the equation above in terms of matrix algebra is given by The letter implies The market value is defined by Market value of i is the equity value of i less the claims of other organizations in the network on i.
represents the fraction of j's primitive assets that i holds directly and indirectly.
The equity value and the market value equations are extended by introducing threshold value