We will review the Watts' friendship cascade model from Watts (2006) and the extension of the Watts' friendship cascade model with random edge weights as specified by Hurd and Gleeson (2012). We will discuss the implecations of cascades in these models when viewed as part of a financial network. Unlike most cascade models, both of these models can be analyzed analytically when the LTIA condition is satisfied. This iterative method as described in Hurd and Gleeson (2012) requires the initial state vector to satisfy the LTIA condition but does not produce a state vector satisfying the LTIA condition as a solution, forcing the initial condition to be remembered throughout the entire process. We propose a Markovian approach towards analysing the extended Watts model by reducing the information contained in the state vector after each iteration. We will demonstrate the ability for this method to analyze cascades models with multiple cascade mechanisms, such as stress, exogenous shocks, and defaults, on a stylized financial network, leading to a more accurate measure of systemic risk.
This is joint work with T. Hurd, and H. Cheng.