Financial networks and systemic risk

Financial institutions establish a wide array of bilateral contracts between themselves that constitute a deeply interconnected complex network. Therefore, whenever a single institution is affected by an external shock, the consequences do not necessarily remain localised, but can reach other institutions and potentially spread to the whole network, a scenario commonly known as systemic risk. Two paradigmatic stylised models that describe such process, Eisenberg & Noe and DebtRank will be introduced. Their derivation will be discussed and their similarities, differences, and limitations pointed out. Finally, the dynamical stability of shock propagation will be discussed, possibly commenting on its relationship with the topology of the network.