1 Introduction
2 Related work
3 Default contagion model
3.1 MMCA model for default contagion
3.2 Dynamical analysis of default contagion
3.3 Dynamical properties of the network: onset slope and sensitivity
3.4 How do sectoral properties of the nodes affect network dynamics?
4 Topological analysis of the client-supplier network
4.1 Network construction
Sector | Size (%) |
\(\overline{k}_{\mathrm{in}}\)
|
\(\overline{k}_{\mathrm{out}}\)
| Default (%) | Rank hub | Rank auth |
---|---|---|---|---|---|---|
Financial institutions | 0.046 | 39.613 | 45.529 | 3.650 | 17 | 1 |
Energy | 0.083 | 12.844 | 8.666 | 1.111 | 14 | 2 |
Financial services | 1.165 | 6.300 | 20.265 | 0.786 | 13 | 3 |
Utilities | 1.529 | 5.589 | 5.903 | 1.264 | 11 | 4 |
Telecoms technology & media | 3.299 | 5.960 | 5.194 | 1.776 | 2 | 5 |
Basic materials | 2.745 | 5.789 | 5.350 | 2.782 | 6 | 6 |
Transportation | 4.064 | 5.411 | 4.336 | 1.868 | 1 | 7 |
Retail | 23.593 | 3.973 | 3.233 | 1.217 | 12 | 8 |
Retailers | 4.273 | 5.001 | 3.613 | 1.885 | 5 | 9 |
Capital goods & industrial services | 8.689 | 4.528 | 3.098 | 1.866 | 9 | 10 |
Autos, components & durable goods | 1.470 | 4.454 | 2.991 | 1.786 | 10 | 11 |
Consumer & healthcare | 7.055 | 3.259 | 3.770 | 1.539 | 8 | 12 |
Construction & infrastructure | 8.907 | 3.067 | 3.270 | 3.071 | 3 | 13 |
Unknown | 10.159 | 0.930 | 1.413 | 1.942 | 15 | 14 |
Real rstate | 6.843 | 1.517 | 1.844 | 3.603 | 7 | 15 |
Leisure | 12.861 | 2.509 | 2.512 | 1.511 | 4 | 16 |
Institutions | 3.219 | 5.547 | 10.764 | 0.535 | 16 | 17 |
4.2 Statistical descriptors
5 Experimental results
5.1 Default incidences for homogeneous recovery rate
5.2 Impact of customer diversification on default incidence
5.2.1 Sector structure-function relationship
Sector |
γ
|
\(I_{\mathrm{in}}\)
|
\(\mathcal{R}_{0}\)
|
\(S_{\mathrm{het}}^{\mathrm{rank}}\)
|
\(S_{\mathrm{hom}}^{\mathrm{rank}}\)
|
---|---|---|---|---|---|
Energy | 1.33 | 13.44 | 1.74 | 1 | 1 |
Financial institutions | 1.27 | 2.39 | 3.81 | 2 | 2 |
Basic materials | 1.58 | 41.07 | 2.89 | 3 | 5 |
Financial services | 1.36 | 1.66 | 2.22 | 4 | 3 |
Transportation | 1.44 | 16.27 | 2.33 | 5 | 4 |
Telecoms, technology & media | 1.44 | 16.99 | 2.68 | 6 | 6 |
Retailers | 1.54 | 28.18 | 2.70 | 7 | 8 |
Capital, goods & industrial services | 1.47 | 9.51 | 2.93 | 8 | 9 |
Utilities | 1.44 | 7.15 | 3.43 | 9 | 7 |
Autos, components & durable goods | 1.52 | 21.24 | 2.82 | 10 | 10 |
Retail | 1.58 | 29.80 | 2.73 | 11 | 11 |
Real estate | 1.40 | 1.86 | 4.74 | 12 | 12 |
Construction & infrastructure | 1.44 | 17.01 | 4.25 | 13 | 13 |
Consumer & health care | 1.55 | 32.06 | 4.10 | 14 | 14 |
Unknown | 1.59 | 5.16 | 3.69 | 15 | 15 |
Leisure | 1.35 | 7.71 | 7.56 | 16 | 16 |
Institutions | 1.54 | 5.65 | – | 17 | 17 |
5.3 Synthetic default assessment experiments
5.4 Validation
6 Discussion
-
We have analyzed the dynamics of default contagion for different values of the recovery parameter μ, dependent and non-dependent on the node’s features. Our methodology allows to tune parameters individually for every company and to carry out experiments for the simulation of future scenarios. In particular, we have studied the impact of the company’s customer diversification on default propagation. A discussion on the connection between topological and dynamical properties is also included (Sect. 5.2.1);
-
Our methodology also allows for another kind of experiment described in Sect. 5.3, where we have focused on the dynamics of default propagation at the transient state, and its dependence on the default initial conditions.