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A NETWORK TOPOLOGICAL 
APPROACH to 
CURRENCY CASCADES 
A thesis presented in fulfilment of the 
requirements for the degree of 
Doctor of Philosophy 
in Finance 
Abstract 
The stability of international financial markets is an important issue for academics 
and policymakers. Crises in currency markets have become increasingly common with 
the 1990s in particular experiencing major episodes of currency turmoil. The causation 
and frequency of these crises is a puzzle, especially for semi-free-floating currencies. 
In this thesis recent currency crises are introduced and examined. Theories and 
methodologies which evolved in complexity and network sciences are then shown to 
have analogies to currency crises and to offer insights for finance. Common factors of 
recent currency crises are shown to be explainable using complexity and network 
sciences, and that price determinant influences exhibit characteristics of a complex 
network. An alternative approach to currency crises based on binary choices using an 
agent-based model in an explicit topological sparsely clustered network is proposed. 
This is shown to be capable of generating complex dynamics, including cascades. 
A proxy topology of currency influences is then extracted from the international 
foreign exchange price matrix and shown to exhibit a robust taxonomy. This topology is 
then subjected to cascade simulation analysis. The results show that node threshold 
values and the density of external links are the key parameters in terms of cascade 
propagation. It is thus shown that a simple parsimonious model of trader interaction 
within a foreign exchange network can produce dynamics which are complex and 
contingent, and match the proposed stylised facts of currency crises. Policy issues 
flowing from these findings are discussed. The results increase our understanding of 
price dynamics in financial markets. 
Acknowledgements 
I would like to begin by thanking my wife, Judith, for her patience, kindness and 
endless support throughout the long period this thesis took. This thesis is dedicated to 
her. I would also like to thank my children, Sean and Caitlin, for their patience in 
accepting that I was not going to play with them yet again. I would also like to thank my 
parents, Peter and Joan, for their continued support and encouragement. 
I am indebted and thankful to Professor Lawrence Rose, Professor Anne de Bruin 
and Dr Brendan Moyle for their excellent supervision, guidance, insight and 
encouragement during the ups and downs of this research. 
I would like to thank Professor Chris Moore for his understanding and the 
Department of Finance's financial support. I would also like to thank Maryke Bublitz, 
Fong Mee Chin and other members of the Departments of Finance, Banking & Property 
and of the Department of Commerce for their ever cheerful help. I would like to thank 
Dr Jonathan Marshall for coming to the rescue with programming support at a critical 
moment, and Prof Nigel French for his useful insights and advice on disease contagion 
and programming. I would like to thank Karen Stanley for graciously proofreading this 
thesis. I would also like to thank the examiners for taking the time to examine this 
thesis. 
11 
Table of Contents 
Abstract 
Acknowledgements 
List of Figures 
List of Tables 
Chapter One Introduction 
1.1 
1.2 
1.3 
International financial market stability 
The Research Question 
The Anticipated Contribution 
Chapter Two Modelling Currency Crises 
2.1 Introduction 
2.1.1 Overview of crisis models 
2.1.2  Developing trader behavioural rules 
2.2 Macroeconomic Feedback Models 
2.2.1 Basics 
2.2 .2 First generation models 
2 .2.3 Second generation models 
2 .2 .4 Problems with the first two generations of models 
2.2. 5  Third generation models 
2.2 .6 General criticisms of macro-feedback models 
2.3 Liquidity and Bank Run Models 
2.4 Micro Structure Models 
2 .4.1 Behavioural fmance models 
2.4.2 Positive and negative feedback models 
2 .4.3 Rational bubble models 
2 .4.4 Information flow models 
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2 . 5  Application of these Models to the Asian Crisis 
2 .5 . 1 The wider Asian crisis 
2 .5 .2  The twin banking/currency crisis 
2 .5 .3  Empirical Research 
2 . 6  Conclusion 
Chapter Three An Alternative Approach 
3 . 1 
3 . 2  
3 . 3  
3 . 4  
Introduction 
Theoretical Issues 
3.2 . 1 
3 .2 .2  
Theoretical foundations 
The power-law distribution 
The Stability ofNetwork Systems 
3 .3 . 1 
3 . 3 . 2  
3 . 3 . 3  
3 . 3 .4 
3 . 3 . 5  
3 . 3 . 6 
Basics 
Cascading failure 
Contagious disease models 
Physical science contagion models 
The dynamics prop?rties of cascades in random networks 
Node centrality and importance 
Currency Crises : A Network Approach 
3 .4. 1 
3 .4 .2 
3 .4 . 3  
3 .4 .4 
Price dynamics in foreign exchange markets 
Trader behavioural assumptions 
Cascades in currency networks 
Theoretical assumptions of a bootstrap binary model 
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3 .4 .5  Sequential agent behaviour in a single decision bootstrap model 49 
3 . 5  
3 .4.6 
3 .4 .7 
3 .4 .8  
Cascade conditions 
A fractional decision model 
Sequencing 
Conclusion 
Chapter Four Topological Methodology 
4 . 1 Introduction 
4. 1 . 1  Overview 
IV 
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4. 1 .2 Outline of methodological issues 57 
4 .2  Methodological Techniques 58  
4.2. 1 Econometric techniques 58  
4.2.2 Hierarchical structure theory 59 
4.2.3 Matrix network theory 62 
4.2.4 Ln-ln diagrams 65 
4.2.5 Eigenvalue analysis 66 
4 . 3  Methodological Summary 67 
Chapter Five Topological Analysis 68 
5 . 1 Introduction 68 
5 . 2  Data Summary 68 
5.2. 1 Introduction 68 
5 .2 .2 Exchange rate data 69 
5 .2 .3 Trade data 70 
5.2.4 FX turnover data 70 
5 . 3  Topological Results 7 1  
5 .3 . 1 Hierarchical structure theory 7 1  
5 .3 . 1 . 1  Introduction 7 1  
5 . 3 . 1 .2 NZD matrix 72 
5 .3 . 1 .3 USD matrix 76 
5 .3 . 1 .4 NZD crisis matrix 80 
5 . 3 . 1 . 5 USD crisis matrix 82 
5 . 3 . 1 .6 Conclusion 83 
5 .3 .2 Matrix network methods 84 
5 .3 .2 . 1 Introduction 84 
5 . 3 .2 .2 NZD 5 link matrix 84 
5 . 3 .2 .3 NZD dichotomised matrix 87 
5 .3 .2 .4 USD dichotomised matrix 89 
5 . 3 .2 .5  NZD crisis matrix 92 
5 .3 .2 .6  USD Crisis matrix 93 
5 .3 .2 .7  Trade matrix 94 
5 .3 .2 . 8  Foreign exchange centre turnover 98 
V 
5 .4  
5 . 5  
5 .3 .3  
5 . 3 .4 
5 . 3 .2 .9 Conclusion 
Eigenvalue analysis 
Power-laws and 1 /fnoise in the MYR market 
Creation of a Proxy Topological Map 
Conclusion 
Chapter Six Simulation Analysis 
6 . 1 Methodology 
6. 1 . 1  Introduction 
6. 1 .2 Simulation Methodology 
6 .2  The Simulation Model 
6 . 3  Experiments with Threshold Parameter Distributions 
6.3 . 1  Results from differing metric on parameters 
6 .3 . 1 . 1  Introduction 
6 .3 . 1 .2 Normal Distribution 
6.3 . 1 .3 Power-law Distribution 
6 .3 . 1 .4 Uniform Distribution 
6.3 . 1 .5 Conclusion 
6.3 .2 Analysis of how many cascades of a given size contain 
a given node 
6 .3 .2 . 1 Introduction 
6 .3 .2 .2 Normal Distribution 
6 .3 .2 .3  Power-law Distribution 
6 .3 .2 .4 Uniform Distribution 
6 .3 .2 .5  Conclusion 
6 .3 .3 Threshold experiment conclusion 
6.4 Experiments with Linkage Densities 
6.4. 1 Introduction 
6.4.2 Changing internal cluster density 
6.4.3 Changing external c luster density 
6.4.4 Conclusions from changing l inkage densities 
6 . 5  Simulation Conclusions 
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Chapter Seven Conclusion 1 3 1  
7. 1 Overview 1 3 1  
7 . 1 . 1  Thesis objectives 1 3 1  
7 . 1 .2 Thesis summary 1 3 1  
7 .2 Summary of Results 1 33 
7 . 3  Contributions 1 34 
7 . 3 . 1 Theoretical contribution 1 34 
7 . 3 .2 Methodological contribution 1 34 
7.3 . 3  Empirical contribution 1 34 
7 .4 Theoretical and Policy Implications 1 35 
7.4. 1 Theoretical implications 1 35 
7.4.2 Pol icy implications 1 37 
7 .5  Model Extensions and Future Work 1 4 1  
Chapter Four Appendix 1 44 
Chapter Five Appendix 1 73 
References 1 83 
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List of Figures 
Figures in main body of text 
Figure 3.1 Regular vs Random vs Clustered Networks 26 
Figure 3.2 Power-law versus Normal Distributions 28 
Figure 5.1 NZD based FX minimum spanning tree (1995-2001) 74 
Figure 5.3 NZD based FX hierarchical tree of subdominant ultrametric 
space (1995-2001) 76 
Figure 5.4 USD based FX minimum spanning tree (1995-2001) 77 
Figure 5.6 USD based FX hierarchical tree of subdominant ultrametric 
space (1995-2001) 79 
Figure 5.12 NZD network graph of binary 5 link distance matrix 85 
Figure 5.14 NZD network graph of dichotomised distance matrix 88 
Figure 5.17 USD network graph of dichotomised distance matrix 90 
Figure 5.19 Crisis period NZD network graph of dichotomised 
distance matrix 92 
Figure 5.24 Network graph of dichotomised trade flows at 5% 95 
Figure 5.26 Network graph of dichotomised trade flows at 10% 97 
Figure 5.33 Derived International Financial Flows Network 102 
Figure 5.34 Simulation Topological Map 104 
Figure 6.7 Effect of varying distributions on threshold parameters 118 
Figures in Appendices 
Figure 5.2 
Figure 5.5 
Figure 5.7 
Figure 5.8 
Figure 5.9 
Figure 5.10 
Figure 5.11 
ln-ln diagram of links in NZD MST graph 146 
ln-ln diagram on links in USD MST graph 146 
Crisis period FX NZD-based minimum spanning tree (1997-98) 148 
Crisis period FX NZD-based hierarchical tree of subdominant 
ultrametric space (1997 -98) 149 
Crisis period FX USD-based minimum spanning tree (1997-98) 150 
ln-ln plot ofUSD-based based crisis MST graph 
Crisis period FX USD-based hierarchical tree of subdominant 
ultrametric space (1997 -98) 
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152 
Figure 5 . 1 3  One-step ego-nets for selected currencies for NZD 5-l ink 
distance matrix 1 53 
Figure 5 . 1 5  In-In plot ofNZD-based dichotomised distance matrix 1 54 
Figure 5 . 1 6  One-step ego-nets for selected currencies for NZD 
distance matrix 1 55 
Figure 5 . 1 8  One-step ego-nets for selected currencies for USD 
distance matrix 1 56 
Figure 5 .20 One-step ego-nets for selected currencies for NZD 
crisis-period distance matrix 1 57 
Figure 5 .2 1  USD-based crisis period network graph of dichotomised 
distance matrix 1 58 
Figure 5 .22 One-step ego-nets for selected currencies for USD 
crisis-period distance matrix 1 59 
Figure 5 .23 In-In plot of countries ranked by export trade 1 6 1  
Figure 5 .25  One-step ego-nets of  trade flows dichotomised a t  5% 1 62 
Figure 5 .27  One-step ego-nets of  trade flows dichotomised a t  1 0% 1 63 
Figure 5 .28  In-In plot of  trade l inks dichotomised at 5% 1 64 
Figure 5 .29 In-In plot of FX turnover by centre 1 66 
Figure 5 .30 Time plot ofMYRJUSD ( 1 990-200 1 )  1 67 
Figure 5 .3 1 Normality comparison for MYRJUSD ( 1 990- 1 998) 1 68 
Figure 5 . 32 MYRJUSD daily change distribution tests 1 69 
Figure 6 . 1 Frequency of cascades starting at a particular node 
normal distribution (Jl = 0 .3 ,  cr = 0.28) 1 75 
Figure 6 .2 Cascade sizes for nodes - normal (0.4) 1 75 
Figure 6 .3  Frequency of cascades starting at  a particular node 
power-law distribution (p = 1 .5) 1 77 
Figure 6.4 Cascade sizes for nodes - power-law distribution (p = 1 . 5) 1 77 
Figure 6 .5 Frequency of cascades starting at a particular node 
uniform distribution 1 79 
Figure 6 .6 Cascade sizes for nodes - uniform distribution 1 79 
Figure 6 .8  Frequency of cascades containing a particular node 
normal (0.3) distribution 1 8 1  
Figure 6 .9 Frequency of cascades containing a particular node 
power-law ( 1 .5)  distribution 1 8 1  
Figure 6 . 1 0  Frequency of cascades containing a particular node 
uniform distribution 1 82 
lX 
List of Tables 
Tables in main body of text 
Table 5.8 
Table 6.2 
Table 6.4 
Table 6.6 
Table 6.8 
Table 6.9 
Table 6.10 
MYR descriptive statistics (1993-2001) 
Normal distribution cascade statistics 
Power-law distribution cascade statistics 
Comparison for uniform, N(0.4), PL (1.2) distributions 
Comparison of node inclusion in cascades 
Effects on global cascades of varying % internal links 
Effects on global cascades of varying % external links 
Tables in Appendices 
Table 5.1 Countries selected for exchange data 
Table 5.2 NZD-based FX distance matrix (1995-2001) 
Table 5.3 Crisis-period NZD-based FX distance matrix (1997-98) 
Table 5.4 Matrix of export trade in country percentage terms 
Table 5.5 Turnover of FX trading by centre 
Table 5.6 Eigenvalue of covariances ofNZD matrix 
Table 5.7 Eigenvalue of covariances of USD matrix 
Table 5.9 MYRJUSD daily change distribution tests 
Table 5.10 MYRJUSD daily change distribution tests (restricted sample) 
Table 5.11 Internal triad linkage density 
Table 6.1 Simulation output for normal distribution (Jl = 0.3) 
Table 6.3 Simulation output for power-law distribution (p = 1.5) 
Table 6.5 Simulation output for uniform distribution 
Table 6.7 Containing simulation output for normal (0.3) distribution 
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