Default Cascades in Scale-free Networks Assessing the role of - - PowerPoint PPT Presentation

Default Cascades in Scale-free Networks

Assessing the role of topology in the emergence of systemic risk Tarik Roukny1,3 Stefano Battiston2 Hugues Bersini1 Hugues Pirotte3

1IRIDIA, Université Libre de Bruxelles 2Chair of System Design, ETH Zurich 3Centre Emile Bernheim, Université Libre de Bruxelles

September 11, 2012

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 1 / 33

Outline

1

Introduction

2

The Model Contagion Dynamics Market’s structure

3

Experiments and Results Validating the model Out-degree distribution Liquidity level

4

Conclusion

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 2 / 33

Introduction

"The Economic Crisis is a Crisis for Economic Theory"

“[...] systematic warnings over more than a century [...] have been ignored and we have persisted with models which are both unsound theoretically and incompatible with data. It is suggested that we drop the unrealistic individual basis for aggregate behavior and the even more unreasonable assumption that the aggregate behaves like such a rational individual. We should rather analyse the economy as a complex adaptive system, and take the network structure that governs interaction into account.” Kirman, 2010

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 3 / 33

Introduction

Complex Systems and Networks

in Complex Systems The inner structure can have an influence on the system’s stability The Internet Albert, Jeong, Barabasi, 2000 Epidemics Pastor-Satorras, Vespignani, 2000 Power Grids Albert, Albert, Nakarado 2004

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 4 / 33

Introduction

Our Question

In Financial Systems

What influence can the network’s structure have on default contagion and systemic risk?

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 5 / 33

Introduction

Background

Litterature Review

1

Empirical studies and stress-test analysis

Italy: (Mistrulli 2005), (Iori et al., 2007) Austria: (Boss et al., 2004) USA: (Furfine et al., 2003) Belgium: (Degryse & Nguyen, 2007) Brazil: (Cont et al., 2011), (Cajueiro& Tabak, 2008) Germany: (Upper & Worms, 2002) etc.

2

Default contagion dynamic models

From models of social influence: (Granovetter, 1978), (Watts, 2002) (Eisenberg & Noe, 2001): fictitious default sequence (Gai & Kapadia, 2010), (Battiston et al., 2012), (Cont et al., 2011)

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 6 / 33

Introduction

In this work

Overview of the Model

Agent-based model

Agents: financial institutions Interactions: credit ties Network: market’s structure

From the analytical model introduced in (Battiston et al., 2012)a

Default cascades in credit networks (e.g. interbank market) 2 channels of contagion:

1

Direct

2

Illiquidity and Panic

Analysis on the impact of risk diversification

aBattiston, S., Gatti, D. D., Gallegati, M., Greenwald, B., and Stiglitz, J. E. (2012).

Default cascades: When does risk diversification increase stability? Journal of Financial Stability 8, 3, 138-149

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 7 / 33

Introduction

In this work

Overview of the Model

Agent-based model

Agents: financial institutions Interactions: credit ties Network: market’s structure

From the analytical model introduced in (Battiston et al., 2012)a

Default cascades in credit networks (e.g. interbank market) 2 channels of contagion:

1

Direct

2

Illiquidity and Panic

Analysis on the impact of risk diversification

aBattiston, S., Gatti, D. D., Gallegati, M., Greenwald, B., and Stiglitz, J. E. (2012).

Default cascades: When does risk diversification increase stability? Journal of Financial Stability 8, 3, 138-149

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 7 / 33

Introduction

Take home message

Contribution to the debate on the optimal architecture of the financial system w.r.t. systemic risk and default contagion No single topology is always optimal regardless of the market conditions Several factors matter:

1

Asset market liquidity

2

Correlation between core-capital and connectivity degree

3

Correlation in-degree and out-degree

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 8 / 33

Outline

1

Introduction

2

The Model Contagion Dynamics Market’s structure

3

Experiments and Results Validating the model Out-degree distribution Liquidity level

4

Conclusion

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 9 / 33

The Model

A F C E B H D G

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 10 / 33

The Model

Financial robustness index ∼ equity ratio ηi = (Ai − Li)/

• j

AN

ij

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 11 / 33

The Model

Contagion Channels - First type

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 12 / 33

The Model

Contagion Channels - First type

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 13 / 33

The Model

Contagion Channels - First type

ηi(t) = ηi(0) − kfi(t) ki

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 14 / 33

The Model

Contagion Channels - First type

ηi(t) = ηi(0) − kfi(t) ki

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 14 / 33

The Model

Contagion Channels

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 15 / 33

The Model

Contagion Channels - Second type

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 16 / 33

The Model

Contagion Channels - Second type

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 17 / 33

The Model

Contagion Channels - Second type

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 18 / 33

The Model

Contagion Channels - Second type

ηi(t) = ηi(0) − kfi(t) ki − b, if ηi(0) < γkfi(t)

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 19 / 33

The Model

Contagion Channels - Second type

ηi(t) = ηi(0) − kfi(t) ki − b, if ηi(0) < γkfi(t)

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 19 / 33

The Model

Contagion Channels - Second type

ηi(t) = ηi(0) − kfi(t) ki − b, if ηi(0) < γkfi(t)

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 19 / 33

Outline

1

Introduction

2

The Model Contagion Dynamics Market’s structure

3

Experiments and Results Validating the model Out-degree distribution Liquidity level

4

Conclusion

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 20 / 33

The Model

Market

Financial robustness distribution p(η(t = 0)) ∼ Gauss(m, σ) Out-degree distributions Homogenous ki = k Erdos-Renyi n − 1 k

• pk(1−p)n−1−k

Scale-Free ck−α

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 21 / 33

The Model

In this work

What is explored

Cascade size for different classes of topology Under different conditions: Level of liquidity Level of connectedness Level of capital structure Under different scenarios Connectivity - robustness correlations Lending - borrowing correlations

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 22 / 33

Outline

1

Introduction

2

The Model Contagion Dynamics Market’s structure

3

Experiments and Results Validating the model Out-degree distribution Liquidity level

4

Conclusion

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 23 / 33

Experiments

Validating the Model

Frontier of large cascades change for Homogenous Random networks (Battiston et al., 2012) Scenario Random individual financial robustness Result Diversification has an ambiguous role

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 24 / 33

Outline

1

Introduction

2

The Model Contagion Dynamics Market’s structure

3

Experiments and Results Validating the model Out-degree distribution Liquidity level

4

Conclusion

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 25 / 33

Experiments

Imposing the out degree distribution

Scenario Random individual financial robustness Result Scale Free is more fragile in illiquid markets

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 26 / 33

Experiments

Imposing individual robustness - degree correlations

Scenario Positive correlation between out-degree and individual financial robustness Results Scale-free has an ambiguous profile: it gets more robust with the connectivity

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 27 / 33

Experiments

Imposing individual robustness - degree correlations

Scenario Negative correlation between out-degree and individual financial robustness Results Scale-free is more fragile

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 28 / 33

Outline

1

Introduction

2

The Model Contagion Dynamics Market’s structure

3

Experiments and Results Validating the model Out-degree distribution Liquidity level

4

Conclusion

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 29 / 33

Experiments

Liquidity impact

Scenario Random individual financial robustness Result Scale-Free is more sensitive to illiquidity increases

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 30 / 33

Experiments

Liquidity impact

Scenario Positive and negative correlations between out-degree and individual financial robustness Results Left: Scale-free reacts better to liquidity increase Right: Scale-free’s stationary phase is higher

Roukny, Battiston, Bersini, Pirotte (ULB) Default Cascades in Scale-free Networks September 11, 2012 31 / 33

Conclusion

What was done

Construction and validation of an Agent-Based Model w.r.t. to an analytical reference Extension to heterogeneous networks

What was shown

Topology has a tricky role

In liquid markets: no significant impact In illiquid markets: impact.. but not unilateral! different topologies have different impact under different conditions

What next

Explore other aspects (robustness distribution, credit distribution) Empirical data

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The End

Thank you for your Attention

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