Contagion! Systemic Risk in Financial Networks (eBook)

Preface 6
Contents 8
1 Systemic Risk Basics 11
1.1 The Nature of This Book 12
1.2 What Is Systemic Risk? 14
1.2.1 Defining SR 15
1.2.2 Haldane's 2009 Speech 16
1.2.3 A Lesson from Network Science: The Sandpile Model 18
1.3 Capital Structure of a Bank 19
1.3.1 Bank Asset Classes 20
1.3.2 Debt and Liabilities 22
1.3.3 Equity 23
1.4 Channels of Systemic Risk 24
1.5 Regulatory Capital and Constraints 26
2 Static Cascade Models 28
2.1 Default Cascades 31
2.1.1 The Eisenberg--Noe 2001 Model 32
2.1.2 Reduced Form E--N Cascade Mechanism 36
2.1.3 The Gai--Kapadia 2010 Default Model 37
2.2 Liquidity Cascades 39
2.2.1 Gai--Kapadia 2010 Liquidity Cascade Model 40
2.2.2 The Liquidity Model of S.H. Lee 2013 42
2.2.3 Generalized Liquidity Cascades 43
2.3 Asset Fire Sales 44
2.3.1 Fire Sales of One Asset 44
2.3.2 Fire Sales of Many Assets 47
2.4 Random Financial Networks 49
2.5 Bibliographic Notes 52
3 Random Graph Models 54
3.1 Definitions and Basic Results 55
3.1.1 Random Graphs 57
3.2 Configuration Random Graphs 58
3.3 Assortative Configuration Graphs 59
3.3.1 The ACG Construction 60
3.3.2 Locally Tree-Like Property 63
3.3.3 Approximate ACG Simulation 67
3.4 Inhomogeneous Random Graphs 69
3.5 Measures of Network Topology 75
3.5.1 Connectivity 76
3.5.2 Measures from the Degree Distributions 76
3.5.3 Centrality Measures 76
3.5.4 Clustering Coefficients 77
3.5.5 Connectivity and Connected Components 78
4 Percolation and Cascades 80
4.1 Branching Processes 81
4.2 Percolation on Configuration Graphs 83
4.3 Site Percolation 87
4.4 Bootstrap Percolation 88
4.5 Watt's 2002 Model of Global Cascades 89
4.5.1 The Framework 89
4.5.2 The Main Result 92
4.5.3 The Cascade Condition 94
4.5.4 The Frequency of Global Cascades 95
4.6 Numerical Experiments on the Watts Model 97
4.7 Extensions of the Watts Model 99
4.8 Dependence in Random Financial Networks 100
4.8.1 The LTI Property 102
4.8.2 Ramifications of the LTI Property 103
5 Zero Recovery Default Cascades 104
5.1 The Gai--Kapadia Model 105
5.1.1 Shocks and the Solvency Condition 106
5.2 The G--K Model with Random Link Weights 109
5.2.1 A Theorem on the G--K Cascade 112
5.3 Measures of Cascade Impact 114
5.4 The Cascade Condition 117
5.4.1 Frequency and Size of Global Cascades 119
5.5 Testing and Using the Cascade Mapping 122
5.6 A New Model for Default Cascades with Asymmetric Shocks 123
5.7 Cascade Computations 127
5.8 Numerical Experiments 129
5.8.1 Experiment 1: Benchmark Gai--Kapadia Model 129
5.8.2 Experiment 2: Assortative Networks 130
5.8.3 Experiment 3: Random Buffers and Link Weights 132
6 Future Directions for Cascade Models 134
Appendix A Background Material 137
A.1 Special Notation 137
A.2 The Discrete Fourier Transform 138
References 140
Index 144