Aims:

Overall, the module represents an introduction to the topic of systemic risk and stress propagation in networked systems. The first part of the module presents a general introduction to complex networks and dynamical processes; the second part is focused on specific applications to the study of contagion in financial networks.Learning outcomes:

On successful completion of the module, a student will be able to:

Compute network metrics and provide a statistical description of networks.
	Analyse dynamical processes on networks.
	Implement simple algorithms for the analysis of financial contagion.
Content:

Introduction to complex networks:

Basic concepts of networks (graphs, subgraphs, adjacency matrix, undirected, directed and weighted networks), common metrics (degree, centrality, clustering, degree distribution, excess degree distribution, mixing patterns, real world examples).
	Network models (random networks, configuration model, small world, preferential attachment).
	Maximum-entropy networks.
Collective behaviour:

Emergence of a giant cluster. Robustness to random and targeted attacks.
	Epidemic spreading processes on networks.
	Cascade processes on networks.
Application to interbank networks and systemic risk:

Interbank networks and their properties.
	Modelling contagion due to counterparty default risk.
	Modelling contagion due to overlapping portfolios and fire sales.
	Identifying systemically important institutions.
	Reverse stress testing.
	Leverage cycles.
Requisites:

To be eligible to select this module as optional or elective, a student must: (1) be registered on a programme and year of study for which it is a formally available; and (2) have familiarity with basic probability and calculus. The coursework assessment will require basic programming skills.

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