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Introduction
The purpose of this research is to investigate how network structures can influence the way that shocks propagate through financial networks and how this may aect policy decisions. For smaller networks, we investigate how the interaction between network structures, liquidity risk and market sentiment can influence the results obtained. By focussing on banking systems, we propose innovative structures to use for simulating the spread of contagion between banks. This is used to show that dierent structures behave dierently under changes to network characteristics and therefore may react dierently to changes in legislation.
The first part of this research is focussed on smaller networks. A new simulation model is developed and used to show how the risk of systemic collapse is aected by dierences in the network structure and other characteristics. While the proposed model is highly simplified, it does incorporate certain real-world mechanics, namely heterogeneity between bank asset sizes, market liquidity losses, investor sentiment, asset maturities, dierences in asset compositions and to some extent real-world lending behaviour. It can thus be considered as more comprehensive and realistic than previously proposed systems. By applying this framework to South African bank balance sheet data, it is shown that the model is capable of detecting increases in systemic risk over time.
The second part of this research is focused on larger networks and therefore makes use of asymptotic results. Known asymptotic results are shown to be applicable to a newly defined, versatile class of stochastic networks. This is then used to make a similar comparison etween network structures as was made for smaller interbank systems.
The rest of this chapter is organised as follows: Section 1.1 discusses the background to the research. Section 1.2 gives a short overview of literature that is relevant in order to motivate the research questions. This includes a brief overview of the necessary network theory background in section 1.2.1. Section 1.3 then elaborates on the purpose and significance of the study, while section 1.4 is used to set out the structure for the remainder of this thesis.
1 Introduction
1.1 Background
1.2 Literature
1.2.1 Background to network models
1.2.2 Relevant literature and motivation for the study
1.3 Purpose and significance of the research
1.4 Structure of the thesis
2 Numerical model
2.1 Simulation method
2.1.1 Network description
2.1.2 Simulation of shock propagation
2.2 Dierent network structures
2.2.1 Definition and standardisation of structures
2.2.2 Characteristics of the proposed structures
2.3 Sensitivities and the eect of dierent network characteristics
2.3.1 Constructing the benchmark system
2.3.2 The efect of varying model parameters
2.4 Application to the South African system .
2.4.1 Overview and adjustments to model
2.4.2 Data and balance sheet construction
2.4.3 Adjusted modelling procedure
2.4.4 Results for the South African system
2.4.5 Additional analyses
3 Asymptotic results
3.1 Background and notation
3.1.1 Network description
3.1.2 Random financial networks
3.1.3 Default and contagion mechanics
3.2 Existing results for deterministic networks
3.2.1 Discussion of relevant functions
3.2.2 Asymptotic fraction of total defaults
3.3 Results for stochastic networks
3.3.1 Results for Erd˝os-R´enyi networks .
3.3.2 Semi-heterogeneous Erd˝os-R´enyi graphs
3.4 Application to stochastic, heterogeneous financial networks
3.4.1 Illustration of theoretical results
3.4.2 Applying the results to dierent network structures
4 Conclusion
4.1 Policy and theoretical implications of results
4.1.1 Network structure sensitivities
4.1.2 Real-world applicatio
4.1.3 Theory and structures for large networks
4.2 Final conclusions
A Numerical model
A.1 Formal tiering test result
B Additional information for South African application
B.1 Additional figures for South African banks’ assets
B.2 Balance sheet information
B.3 Network properties of the South African system
B.4 Changing the risk measure
B.5 Additional analyses figures
B.5.1 Risk quantities over time by size category
B.5.2 Risk quantities vs. asset values
B.5.3 Risk quantity distributions
C Asymptotic results
C.1 Network resilience and susceptibility
