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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.

Intended learning outcomes:

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

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

Indicative content:

The following are indicative of the topics the module will typically cover:

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 assessment will require basic programming skills.