Analyzing Financial Institution Resilience using Complex Network Theories

This research paper analyzes the financial institution resilience using complex network theories and Monte Carlo simulations to assess different networks and topologies through the contagion model. It also examines the interplay of imperative drivers of interbank contagions like interconnectedness, network topology, homogeneity, and leverage throughout the bank sizes and exposures of the interbank.

STATISTICS R

Table of Contents
Abstract................................................................................................................................................2
Introduction.........................................................................................................................................2
Measuring systemic.............................................................................................................................4
Mark-to-Market Values....................................................................................................................11
Primitive Assets, Organizations, & the Cross-Holdings.................................................................13
Values of Organizations....................................................................................................................14
Discontinuities in the Values and the Costs of Failure....................................................................14
Existence of Equilibrium and Multiplicity......................................................................................15
Integration and Diversification.........................................................................................................15
Stochastic Block Model.....................................................................................................................15
Random Networks.............................................................................................................................16
The Consequences of Diversification................................................................................................18
Conclusion..........................................................................................................................................19
References..........................................................................................................................................19

Abstract
The main aim of this research is to analyze the financial institution resilience to
determine the techniques that have been employed in complex network theories. The study is
carried out using the Monte Carlos simulations to assess the different networks as well as the
topologies through the contagion model that is applicable in diverse interbank networks. The
banking series is triggered.
We researched a series of different banking crises through each bank in the device and
examined the mechanisms used for propagation which take impact’s the device’s internal
distinctive scenarios. At last, a literature review is conducted to examine the interplay of the
countless imperative drivers of interbank contagions like the interconnectedness, network
topology, homogeneity and leverage throughout the bank sizes and the exposures of the
interbank.
Introduction
The national economy’s complexity has crystal rectifier with several lecturers, for
utilizing the network theory in order to review the results of connectedness and configuration
on money stability. Finding out the national economy as a network is one of the ways which
is accustomed to investigate the general risk’s emergence via the connections of the banks. In
this type of a network structure, each node signifies a bank. Therefore, the links between the
banks area unit is portrayed by the edges. An active interbank market acts as the bond in the
national economy’s stability.
The interbank market’s use has enabled the banks that suffer the shortage of liquidity
to borrow from the banks which have surplus liquidity. Hence, on the national economy, the
interbank market will have an effective result by efficiently sharing the money with the
banks. But, consequently it will make the system vulnerable to the monetary contagion due to
the present linkages of the interbank. For many years, the giant financial establishments were
included as the assorted suspects to destabilize the national economy, whose failure could be
fatal for the bigger national economy (as it is too massive for the fail theory). The
government should support such monetary establishments once they face fiscal distress
because of their general importance and link.
However, if they fail, the smaller money establishments with ample connections
within the interbank market will have an excellent, and highly significant effect on the

financial set-up. The interbank network’s higher links will scale back the chance of default,
because several counterparties share transmission of a shock and so it disperses quickly. In
contrast, once the excitement’s magnitude has crossed a vital threshold due to the increase in
connectedness the collapse can unfold into an oversized part of the system then it might cause
defaults in an oversized cascade. Thus, this can be a questionable "robust-yet-fragile"
property which is exhibited by the money systems.
This paper therefore focuses on the direct contagion channel and studies the
effectiveness of varied drivers on the interbank contagion. The flourishing literature which is
derived until today has helped to develop the theoretical models which aims to address the
assorted problems regarding general risk. Contrary to fact simulations on information are
utilized to check interbank contagion beneath completely different eventualities associated
with the interbank network’s topology, the scale of interbank exposures. Therefore, the
degree of heterogeneousness and interconnection among the system. This research tends to
develop a model with the banks connected to one another based on the claims of the
interbank and is investigated with the help of Monte Carlo simulations, however, the
complexness of an interbank network structure impacts the interbank contagion beneath
completely different testable eventualities. This analysis belongs to a part of the theoretical
literature, as we tend to use laptop simulations to construct an oversized range of bank
networks involving entities by closing down bank claim and obligations. Victimization tools
from the complicated network theory’s aim is to develop a model; however, the reaction of
the AN initial default might also unfold from one establishment to a different.
Second, we tend to utilize solely two parts based on the records of a bank, which
includes the equity and loans of the interbank for constructing a penurious regression model.
The regression model has been employed to test the crucial impact drivers recorded in the
experiments regarding simulations experiments on the interbank. Multivariate analysis is also
conjointly utilized by Krause and Guarantee for assessing the role contend by the network's
topological options and record the positions within the transmission of bank failures. The
authors use a model which is a scale-free network model for reviewing the interbank
contagion with massive parameter ranges, and a plenty of parameters for initializing the
record. But, their model becomes inflexible in terms of operation, because it is tough for
checking the simulations by the variable one amongst the settings.
In contrast, this model is well understandable, reproducible and additionally it is
amenable for the interpretation and analysis. We tend to outline the term contagion because
the state of affairs within that the bank’s initial failure ends up as a failure of a minimum of

one different bank, whereas the extent of contagion is measured based on the complete
financial loss within the banking industry, because of at least one bank’s inability. On the
other hand, we tend to the area unit principally inquisitive about sleuthing the capital losses’
magnitude within the banking network instead of various banks which were impacted highly.
At last, this paper helps to present the prevailing literature which is examined by using a
comprehensive network model, the knock-on effects. AN initial default will bring into the
interbank network below the idea of randomness.
The idea which the interbank network claims and obligations forms indiscriminately,
allows North American country to capture all potential eventualities that will seem in the
real-world things. Additionally, we tend to avoid the matter knowledge of information
inconvenience as a real data on the exposures area unit of the interbank typically is solely on
the market to central bankers and the regulators, so renders the problematic network’s
empirical analysis.
This research’s findings represent that the heterogeneousness in size of the banks and
interbank exposures matter an excellent deal within the financial set-up’s stability, because its
absorption capability is increased. Additionally, the extent of connectedness vastly affects the
resilience of the system, particularly in smaller and extremely interconnected interbank
networks. At last, a proof is provided that extremely leveraged the type of banks the most
channel through that monetary shocks propagate at intervals the system, and similar result is
additionally pronounced in the massive interbank networks when compared to the smaller
banks.
The remaining paper is subdivided into two sections to discuss the connected
literature on the interbank contagion. Chapter three presents the network model of contagion.
Measuring systemic
A network model projected by Eisenberg and Noe comprises of 3 essential ingredients
namely, a group of n nodes N ¼ f1; 2; ... ; ng, associate n liabilities matrix P ¼ wherever
FTO P zero denotes the due payment from the node i to node j; pii ¼ zero, and a vector c ¼
ðc1; c2; ... ; cnÞ two Rn þ wherever ci P zero represents the worth of outdoor assets control
by node i additionally to its claims on alternative nodes within a network. Generally, ci
comprises of money, mortgages, securities, and alternative applications on the external
entities of a system. Additionally, every node i could have liabilities for the external entities
from the network; we tend to let metallic element P zero represents the total of all similar
obligations of i, that we tend to accept to have equivalent priority with i's liabilities for the

alternative nodes within a network. The quality facet of the node i's record is provided by ci þ
P j–ipji, and therefore the liability facet is provided by pi ¼ metallic element þ P j–pig. Its
web value is that the distinction Badger State ¼ ci þX j–ipji pi: ð1Þ the notation related to the
generic node I, which is represented in the Figure 1. Within a network (indicated by the
dotted line), node I have associate obligation FTO to the node j and also has claim PKI on the
node k. This figure additionally depicts the node I's external assets ci and outdoors liabilities
metallic element. The distinction between the total assets and the total liabilities is that the
node's web value Badger State.
Observe that the I's web value is unrestricted in sign; if it's plus in such case it
communicates to the I equity’s value. We tend to decision the "book price" as a result of it's
supported the nominal or face value of the pji liabilities, instead of the ''market" values which
replicate the ability of the nodes to pay. These market prices rely on the ability of the
alternative nodes to pay the conditional on the realized value of their external assets.
Specifically, let every node's external assets be subjected to a random shock which decreases
the worth of its external assets, and similarly impacts the web value. This area unit shocks the
"fundamentals" which propagates via a network of monetary obligations.
To illustrate the result of a shock, we tend to think about the numerical, that follows
the notational conventions. Above all, the central node includes a web value often as a result
of its one hundred fifty in outside assets, a hundred in the external liabilities, and forty in
liabilities to the alternative nodes within a network. A shock of magnitude ten to the surface
assets deletes the web value of the central node, however, leaves it with only sufficient assets
(140) to cowl its liabilities. A shock of magnitude eighty leaves the primary node with the
assets of seventy, [*fr1] the worth of its liabilities. Below a pro-rata allocation, every liability
is cut in [*fr1]. Therefore every peripheral node gets the payment of five that is simple to
balance assets and liabilities of every peripheral node. Hence, during this case, there exists
central node defaults; however, the peripheral nodes don't. A shock to the primary node's
external asset is bigger when compared to eighty, which could scale back the worth of each
node's assets that is lower than the value of its liabilities.
> library(NetworkRiskMeasures)
> ME <- matrix_estimation(rowsums = A, colsums = L, method = "me")

Starting Maximum Entropy estimation.
- Iteration number: 1 -- abs error: 2.0356
- Iteration number: 2 -- abs error: 0.0555
- Iteration number: 3 -- abs error: 0.004
- Iteration number: 4 -- abs error: 3e-04
Maximum Entropy estimation finished.
* Total Number of Iterations: 4
* Absolute Error: 3e-04
> ME <- round(ME, 2)
> ME
a b c d e f g
a 0.00 2.53 2.18 0 0 0.74 1.55
b 1.72 0.00 1.60 0 0 0.54 1.14
c 0.98 1.06 0.00 0 0 0.31 0.65
d 0.25 0.27 0.23 0 0 0.08 0.17
e 0.75 0.81 0.70 0 0 0.24 0.50
f 0.00 0.00 0.00 0 0 0.00 0.00
g 0.30 0.32 0.28 0 0 0.09 0.00
>set.seed(192)
> MD
a b c d e f g
a 0 3 0 0 0 0 4
b 3 0 2 0 0 0 0
c 0 2 0 0 0 1 0
d 0 0 0 0 0 1 0
e 0 0 3 0 0 0 0
f 0 0 0 0 0 0 0
g 1 0 0 0 0 0 0
> data("sim_data")
> head(sim_data)
bank assets liabilities buffer weights

1 b1 0.37490927 9.6317127 5.628295 17.119551
2 b2 0.66805904 0.7126552 2.847072 6.004475
3 b3 0.79064804 0.3089983 3.983451 6.777531
4 b4 0.02420156 0.6562193 5.657779 7.787618
5 b5 0.65294261 0.9153901 4.446595 8.673730
6 b6 0.60766835 0.3007373 2.252369 4.708805
> summary(contdr)
Contagion Simulations Summary
Info:
Propagation Function: debtrank
With parameters:
data frame with 0 columns and 0 rows
Simulation summary (showing 10 of 125 -- decreasing order of additional stress):
b55 0.1102 0.280 58.4 235.8 17
b28 0.0638 0.182 63.5 99.3 8
b84 0.0236 0.117 7.6 65.7 2
b69 0.0133 0.114 13.0 36.6 2
b75 0.0099 0.113 9.6 30.5 2
b33 0.0243 0.088 27.4 33.6 2
b120 0.0099 0.077 8.4 18.1 2
b77 0.0067 0.065 9.4 8.9 1
b74 0.0161 0.064 14.4 27.9 3
b101 0.0070 0.060 9.3 17.1 2
> plot(contdr)
Contagion Simulations Summary
Info:
Propagation Function: threshold
With parameters:
data frame with 0 columns and 0 rows

Simulation summary (showing 10 of 125 -- decreasing order of additional stress):
b55 0.1102 0.273 58.4 221.1 16
b28 0.0638 0.167 63.5 88.4 7
b84 0.0236 0.098 7.6 62.0 2
b69 0.0133 0.096 13.0 34.1 2
b75 0.0099 0.095 9.6 28.1 2
b120 0.0099 0.075 8.4 17.0 2
b27 0.0173 0.059 20.5 18.8 3
b74 0.0161 0.056 14.4 26.1 3
b101 0.0070 0.052 9.3 15.6 2
b80 0.0084 0.051 9.2 7.5 1
>contthr_summary<- summary(contthr)
>sim_data$cascade<- contthr_summary$summary_table$additional_stress
> head(sim_data)
bank assets liabilities buffer weights degree btw close eigen alpha impd
1 b1 0.37490927 9.6317127 5.628295 17.119551 3 158 6.285375e-04 0.014737561 63.574054
2 b2 0.66805904 0.7126552 2.847072 6.004475 2 0 6.556480e-05 0.009530187 1.439016 0.00000
3 b3 0.79064804 0.3089983 3.983451 6.777531 2 6 6.609795e-05 0.004553244 1.180453 0.00000
4 b4 0.02420156 0.6562193 5.657779 7.787618 3 802 6.431771e-04 0.002843708 16.669921 0.0000
5 b5 0.65294261 0.9153901 4.446595 8.673730 2 14 6.609864e-05 0.003889006 2.945919 0.00000
6 b6 0.60766835 0.3007373 2.252369 4.708805 2 2 6.556680e-05 0.001567357 1.287698 0.00000
DebtRank cascade
1 0.0278774471 0.0187702836
2 0.0015547276 0.0014304155
3 0.0005985364 0.0005137390
4 0.0074578714 0.0023841317
5 0.0093804082 0.0076966953
6 0.0009334068 0.0005486289
> rankings <- sim_data[1]
> head(rankings, 10)

bank DebtRank cascade degree eigenimpd assets liabilities buffer
55 b55 1 1 1 1 1 40 1 2
28 b28 2 2 3 18 2 85 2 1
84 b84 3 3 8 4 5 78 3 29
69 b69 4 4 12 9 5 95 8 7
75 b75 5 5 15 15 5 46 12 9
33 b33 6 17 9 58 18 51 4 3
120 b120 7 6 13 46 7 59 11 23
77 b77 8 29 15 63 21 101 28 11
74 b74 9 8 8 31 10 86 5 5
101 b101 10 9 13 74 15 113 25 13
>cor(rankings[-1])
DebtRank cascade degree eigenimpd assets liabilities buffer
DebtRank 1.00000000 0.93231850 0.3842379 0.4768787 0.60635065 -0.069485591 0.844166766
cascade 0.93231850 1.00000000 0.4070260 0.5430477 0.62448228 -0.010841119 0.858208779
degree 0.38423792 0.40702597 1.0000000 0.5332633 0.52451198 0.415204147 0.399596081
eigen 0.47687869 0.54304771 0.5332633 1.0000000 0.49012583 0.441087558 0.512325653
impd 0.60635065 0.62448228 0.5245120 0.4901258 1.00000000 0.018459808 0.610921083
assets -0.06948559 -0.01084112 0.4152041 0.4410876 0.01845981 1.000000000 0.004958525
liabilities 0.84416677 0.85820878 0.3995961 0.5123257 0.61092108 0.004958525 1.000000000
buffer 0.43730120 0.39536923 0.2552769 0.1465438 0.48165762 -0.119827957 0.393026114
> summary(cont)
Contagion Simulations Summary
Info:
Propagation Function: debtrank
With parameters:
data frame with 0 columns and 0 rows
Simulation summary (showing 10 of 25 -- decreasing order of additional stress):
23 pct shock 0.23 0.25 182 179 14
22 pct shock 0.22 0.25 174 173 13

21 pct shock 0.21 0.25 166 167 12
24 pct shock 0.24 0.25 190 185 15
20 pct shock 0.20 0.25 158 161 11
25 pct shock 0.25 0.25 198 191 16
19 pct shock 0.19 0.25 150 155 10
18 pct shock 0.18 0.25 142 149 10
17 pct shock 0.17 0.24 134 142 10
16 pct shock 0.16 0.24 127 136 10
> plot(cont, size = 2.2)

Mark-to-Market Values
A usual method of deciphering p(x) is a method which relates to the payments that
balances the realized assets and liabilities at every node provided that:
1. The debts take precedence over the equity.

2. All the debts at a provided node area unit is written down proportionately once
Infobahn assets at that node (given the payments from others), is shy for
fulfilling its obligations.
On the other hand, a second method of deciphering visualizes as a mark-to-market
valuation of all the assets following a system shock. The value pi of node i's liabilities are
marked right down in a consequence of the shock x, together with its effect on the alternative
nodes. As per our discussion on top of, when marking-to-market, node i's internet value is
decreased. The reduction in internet value exhibits each direct result of the shock element xi
and also the indirect impacts of the complete shock vector x. Note, but this is often an
announcement concerning values; it doesn't require the payments to be created at the tip of
the amount. Underneath this interpretation gives a regular re-evaluation of the assets and
liabilities of each node once the shock x happens.
Calculating contagion’s probability
The Systemic risk is often practically divided into a couple of components such as the
following:
a) The chance that a provided set of nodes D can be default.
b) The loss in price conditional on D is the default setting.
This decomposition permits the U.S. to tell apart between 2 distinct phenomena
namely, contagion and amplification. Contagion happens once the defaults by some nodes
trigger defaults by the alternative nodes via an upshot. The amplification happens once the
contagion ends; however, the losses amid the defaulting nodes keep increasing owing to their
financial obligation to at least one another. This means that the primary result reflects to
"widening" of the crisis, however the second reflects to ''deepening" of the crisis.
The purpose of this section is evaluate the chance of contagion; the ensuing chapter
deals with the amplification of losses because of the impacts of the network. For estimating
the likelihood of contagion, we have to be compelled to create assumptions concerning the
distribution of shocks. However, the relative chance of contagion versus synchronal direct
default will be estimated with {virtually|nearly|just concerning} no information about the
network structure and comparatively weak conditions on the shock distribution. For
formulating the results, the following notation is used. Let the atomic number 83 ¼ ðpibiÞ=pi
be the proportion of i's liabilities to alternative entities within the financial set-up, that we
tend to shall decision i's commercial property. 8 we will assume that atomic number 83 >0
since otherwise node i'd effectively be outside the financial set-up. Recall that Wisconsin is

i's initial internet value (prior to the shock), and ci is that the initial price of its outside assets.
The shock Xi to node i takes values in ½0; ci. Assume wi> 0, since otherwise, i'd already
been insolvent. We conjointly think that Wisconsin is half dozen ci, otherwise; i might never
default directly through losses in its external assets. Outline the magnitude relation ki ¼
ci=wi P one to be the leverage of i's external assets. (Thus, it isn't similar to i's total leverage,
which in our language is the magnitude relation of i's total holdings to i's internet value.)
Primitive Assets, Organizations, & the Cross-Holdings
There exists n organizations (for instance, banks, countries, or the firms) creating a
collection N =. The value of the organizations have eventually supported the benefits of the
primitive assets or the factors of production – from currently on mere assets – M =. For
corporeality, a primitive quality is also thought as a project which produces the internet flow
of money over time.6 the current price (or the market price) of quality k is represented as pk.
Let Dik ≥ zero be the share of the worth of quality k command by (that is by directly flowing
into) the organization i, and let D signify the matrix whose (i, k)-th entry is till Dik. (For all
the matrices, the analogous notation is employed) A company could even hold the shares of
different organizations. For any i, j ∈ N, the quantity Cij ≥ zero is that the fraction of the
organization j closely-held by the organization i, wherever Cii = zero for every i. 7The matrix
C will be considered as a network inside which exists a directed link from j to i if price flows
in this direction – i.e., if i owns the decisive share of j, thus Cij> zero.8.
After accounting all the cross-holding shares, the leftover is a share Cbii := one − P
j∈NCji of organization i not closely-held by any organization within a system – a share is
assumed to be positive.9 this can be the half that's closely-held by the external shareholders
of i, external to the cross-holdings’ system. The matrix Cb’s off-diagonal entries are outlined
as zero. According to the cross-holdings’ interpretations, modelling of linear dependencies is
selected. We tend to read them as AN approximation of debt contracts around the
organizations' failure thresholds – where we concentrate on the value of the organizations.
During this, there is a linear assignation in what proportion of the debt is paid back; the
approximation of debt contracts by a linear system is illustrated in Figure ten in Section 10.1
within the Supplementary Appendix. A lot of usually, cross-holdings will involve all styles of
arrangements; any liability within the sort of some payment, which is because it may be
enclosed. Directly modeling different methods of getting among the organizations might
increase the complexities in the analysis, and then this formulation is concentrated, for
example, the essential problems.

Values of Organizations
In a cross-holdings setting, there exists the subtleties for deciding a "fair market"
worth of a corporation, and also evaluates the real economic prices of the organizations'
failure. Thus, it is essential to do accounting properly, as it is crucial to analyze the cascades
of the failure, and it acts as an essential framework for accounting. During this section, we
tend to briefly review the accounting and also perform critical valuation in the absence of the
failure prices. The succeeding chapters incorporate the failures and its connected
discontinuities. The equity worth Vi of a corporation i is the total value of its shares – those
command by alternative organizations moreover as they are held by the external
shareholders. This often depends on the value of the organization i's primitive assets, and its
claims’ value on the alternative organizations.
Discontinuities in the Values and the Costs of Failure
The essential part in this model refers to the organization, which will lose its
productive price in a discontinuous way, if its value falls below the bound crucial thresholds.
Such discontinuities will result in cascading failures and results in the presence of multiple
equilibria. There are several sources for such discontinuities. As an example, if the associate
airline will not pay money for the fuel, then its planes are also forced to take a seat idle that
ends up in discontinuous visit revenue as a result of losing the new bookings. If a firm's debt
rating is downgraded, then its value of capital typically experiences a discontinuous jump in
(Kallio and Khabazian, 2018).
Dropping below an essential price may additionally contains the bankruptcy
proceedings and the fair prices. Mostly, various discontinuities rise from the illiquidity that
ends up in inefficient usage of assets. Additional usually, providing economic production will
comprise a spread of synergies and complementarities, any interruption within the ability to
pay money for and acquire certain production factors which will result in discontinuously
inefficient usage of diverse factors, or investments. If the value vi of an organization i falls
below some strength vi, then i is claimed to fail and incurs failure prices βi . 1This introduces
essential non-linearity – so, discontinuities – into the system. It is necessary to stress that the
failure prices support the (market) price of a company, vi, and not the value, Vi. Failure
happens once a company has difficulties or disruptions inoperative, and therefore the
artificial inflation in the book values which accompanies the cross-holdings is moot to avoid
the threshold of failure. The cross-holdings are necessary for deciding whether or not a

failure threshold is hit, however thanks to their impact on particular values of the
organizations, and not on their book values.
Existence of Equilibrium and Multiplicity
For the organization values in equation (5), the solution is associated to the degree of
equilibrium set of values, and encapsulate the cross-holdings network during a clean and
powerful kind, and build a dependency matrix A. There always exists an answer and there are
various solutions to the valuation equation within the existence of the discontinuities. A set of
solutions develops a whole lattice. There exists a couple of different sources of equilibrium
multiplicity. First, take the alternative organizations' values and therefore, the benefits of the
underlying assets as mounted and provided, and there are various attainable consistent values
of the organization i which solves the equation.
Integration and Diversification
It is said that, the national economy becomes additional heterogeneous once the
number of cross-holders in every organization i weak will increase, and also the cross-
holdings of all the original cross-holders of i weakly decreases. Therefore, the role of
integration is to capture the depth or extent of organizations' cross-holdings. This may be
viewed as an intensive margin. In distinction, diversification pertains to the number of
organizations interacting directly with another and then is an intensive margin. It's potential
for an amendment in cross-holdings to each increase diversification and integration. There
are changes in cross-holdings that increase diversification; however, not integration and
different modifications that increase synthesis but not diversification.
Stochastic Block Model
The exaggerated diversification and increased integration affects various
organizations which fail in an exceeding cascade following the failure of one organization's
assets, we tend to specialize in the model. Every organization contains precisely one
proprietary quality where m = n and D = I. Thus, it keeps the analysis unlettered and permits
the U.S. to specialize in the network of cross-holdings. To keep it simple, we tend to
conjointly begin with quality values of pi = one for all the organizations and have standard
failure thresholds vi = θvi, for a parameter θ ∈ (0, 1), wherever vi is the beginning price of
the organization i once all the assets are at the value one. If a corporation fails, it loses its full
price such that βi = vi (without going negative28 if vi The cross-holdings are taken from the
adjacency matrix G with the entries in {0,1}, where Gij = 1 represent that i contains the

cross-holdings in j and sets Gii = zero. A fraction c of every enterprise is held using different
organizations, which are evenly spread among the di = P j Gji groups that contain it.
The remaining one − c of the organization is command by its external shareholders
such that Cbii = one − c. Holding c fastened, as dj will increase, various organizations
containing the cross-holdings in j will increase; however, each of these organizations have
lower cross-holdings in j. Hence, during this model, the diversification will increase by
increasing dj and not the integration. Holding the underlying graph G fastened, then as c will
increase every organization will have lower self-holdings; however, the higher cross-holdings
within the alternative organizations are already owns it. So increasing c will increase
integration, however, not diversification. In short, this can be an easy constant quantity model
that permits the USA to vary integration and diversification singly.
Random Networks
For illustrating the results of the growing diversification and the growing integration
on the cascades, the setting the place connections between the agencies is seen which are
formed randomly with each agency containing cross-holdings in a random set of different
organizations. Particularly, a directed, undirected graph is structured with every directed
hyperlink having likelihood d/ (n − 1) so that the expected in degree and out degree of any
node is d. Precisely, the adjacency matrix of the design refers to a matrix G (which is not
symmetric anymore), the place Gij for i 6= j are i.i.d. Bernoulli random variables take fee 1

with probability d/(n − 1) and zero otherwise. For studying the consequences of the growing
diversification and the growing integration (i.e., increasing d and decreasing c respectively),
An organization’s proprietary asset failing is simulated and files a wide variety of businesses
which fail in the ensuing cascade.

The Consequences of Diversification
For our simulations, we tend to think about n = one hundred nodes and the work with
a grid on the expected degreed between one and twenty. We tend to work with the values of θ
∈ [0.8, 1]. The 1st exercise is to change the diversification amount, whereas holding different
variables mounted and to examine however the quantity of organizations (among hundred
organization) which fail differs based on diversification. The Figures 3a and 3b are depicts
the proportion of organizations which fail the changes because of the level of diversification
(d) is different (fixing integration at c = zero.5). For a typical level of the failure threshold,
the result is (θ = zero.93). We tend to see a non-monotonicity quite clearly. Once d is
adequately low, 3 or below, in such case we tend to see the share of organizations whose
failure is a smaller amount than twenty. In such case, the network isn't connected; a typical
organization has direct or indirect connections via cross-holdings to solely a little fraction of
others, and any contagion is often restricted to a small part. As d will increase, then we tend
to see the substantial cascades poignant the organizations’ giant percentages.
The network of cross-holdings comprises of a couple of fundamental properties: it's
typically connected29, and corporations still holds giant cross-holdings in different individual
organizations, thus contagion will occur. It can be the "sweet spot", wherever the ingredients

II and III are gift and robust – contagion is feasible, and there's enough interconnection for a
cascade to unfold. As we tend to increase diversification still, the extent of waterfalls is falls,
as diversification is currently lowering the possibility that contagion happens. The summary
states that, there is perpetually a trade-off between II and III, however, at the start III
dominates as diversification ends up in dramatic changes within the connectedness of the
network. Next, II dominates: as the system is connected, the most limiting force is that the
extent to the failure of 1 organization sparks the failures in others that is decreasing with the
diversification. These 3 regimes are depicted in the Figure 4. The Figure 3b illustrates that
these impacts differ with θ, i.e., when the higher values of θ correspond with the higher
failure thresholds, and then it becomes easy to trigger the contagions. This will increase
within the curves for all the levels of diversification. Increasing in θ ends up in a new fragile
economy across the board.
Conclusion
A model of contagion in discretional menial networks is developed, which represents
the issues concerning the widespread transmission of shocks in the associate era of rapid
financial globalization, and within the rise of a significant general economic crisis. This
model generally relates to the agents’ systems connected along by their commercial claims on
one another, as well as through interbank markets and payment systems. Whereas high
property might cut back the chance of contagion, it may also increase it’s unfold once issues
occur. The adverse combination shocks and liquidity risk additionally amplifies the
likelihood and extent of the contagion. The found results counsel that the financial systems
might represent a robust-yet-fragile tendency. Additionally, it highlights that the priori twin
shocks will have immensely totally diverse consequences, that helps make a case for why the
proof of the system resilience to reasonably massive shocks before the year 2007 wasn't a
reliable guide for its later durability.

References
Kallio, M. and Khabazian, A. (2018). Cooperative Mitigation of Contagion in Financial
Networks. SSRN Electronic Journal.