thestabilityofbankingsystemwithshadowbankingondifferent interbank … · 2020. 12. 21. ·...

Research ArticleTheStabilityofBankingSystemwithShadowBankingonDifferentInterbank Network Structures

Hongjie Pan and Hong Fan

Glorious Sun School of Business and Management Donghua University Shanghai 200051 China

Correspondence should be addressed to Hong Fan hongfandhueducn

Received 21 December 2020 Revised 19 January 2021 Accepted 27 March 2021 Published 10 April 2021

Academic Editor Marcelo A Savi

Copyright copy 2021 Hongjie Pan andHong Fan+is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

With the rapid development of the financial market the outbreak of systemic risk is affected by many factors among which shadowbanking is considered to be the essential reason to cause financial crisis and destroy the stability of the banking system In view of thestability of the banking system considering shadow banking interbank lending and complex relationships between banks adynamic complex interbank network model with shadow banking under different network structures is proposed Based on themodel the effects of ROI investment periods average deposit deposit interest rate the density of shadow banks and asset loss arestudied quantitatively and the sensitivity and difference of the banking system with shadow banking under different interbanknetworks are compared and analyzed +e findings indicate that the spread of systemic risks between banks is closely related to theinterbank network structuresWith the relatively concentrated interbank network structure it is easier to increase the probability anddegree of risk contagion Under the random small-world and scale-free networks the random network has the strongest ability toresist and absorb risks while the small-world network is the weakest However once the banking network suffers a big shockexcessive risk will directly break through the protection of the banking network detonate the systematic risk and destroy the stabilityof the banking system with shadow banking +is study contributes to a future empirical research agenda on the topic Moreover itgives a reference for policymakers and regulatory authorities to prevent systemic risk introduced by shadow banking

1 Introduction

Banking system is a crucial part of modern finance and anindispensable financial subject for maintaining the stableoperation of the financial system +rough the interbankmarket complex relationships in the form of lendingpayment settlement discount acceptance guarantee andso on are formed by banks On the one hand such complexrelationships can make up for the liquidity shortage of bankson time and maintain the stability of the banking system[1 2] On the other hand once a certain bank in the system isimpacted and goes bankrupt this risk will also be trans-mitted to other banks through the complex interbank re-lationships having an effect on the banking system [3 4]+erefore the complex relationship is one of the key factorsthat cause the fluctuation of the banking system Employingthe complex network theory to describe the interrelationshipamong bank agents and constructing the complex network

of the interbank market has aroused extensive attention ofscholars

In the context of global banking crises as a carrier offacilitating liquidity exchange [5] and a potential path forrisk contagion [6 7] the interbank network plays a non-negligible role in maintaining the stability of the bankingsystem [8] Existing research mainly focuses on the inter-bank network structure [9 10] For example Allen and Gale[11] established a financial contagion model and pointed outthat when the banking system faces liquidity shocks thecomplete market structure can achieve the optimal risk-sharing of the system better than the incomplete interbankstructure Casser and Duffy [12] confirmed that the riskcontagion speed of the local interbank network is slowerthan that of the globally interbank network but the liquiditylevel in the system is lower Duffy et al [13] consideredcomplete versus incomplete networks of banks and foundthat the complete network structure is significantly less

HindawiDiscrete Dynamics in Nature and SocietyVolume 2021 Article ID 6650327 15 pageshttpsdoiorg10115520216650327

vulnerable to financial contagions than the incompletenetwork structure under a high liquidation cost Aleksiejuket al [14] proposed a two-dimensional directed interbanknetwork model and found that there is a critical thresholdfor the average concentration of interbank deposits and theprobability of bank failure at the threshold obeys a power-law distribution Iori and Jafarey [15] built an interbanknetwork model based on random networks and stressed thatthe homogeneous interbank market makes the bankingsystem more stable while heterogeneous banks may cause achain reaction of contagion between banks Nier et al [16]also constructed a simple hierarchical network model basedon random networks and observed that a more centralizedbanking system is often more fragile Linardi et al [17]analyzed the interbank network using a dynamic latent spaceapproach and captured the core-periphery structure of fi-nancial networks By investigating the impact of the bankingnetwork structure market liquidity and idiosyncraticshocks on the stability of the banking system Gai andKapadia [18] pointed out the banking system exhibited arobust-yet-fragile tendency Moreover Lenzu and Tedeschi[19] established an agent-based interbank network modelwhich compared the stability of the banking system underthe structure of the random network and the scale-freenetwork +e results showed that in the case of heteroge-neity the random network structure is more stable than thescale-free network structure Caccioli et al [20] analyzed theeffect of different interbank network structures on the sta-bility of the banking system and found that the scale-freenetwork has better flexibility but its stability with regard tothe banking system is also significantly lower than othernetworks Zhang et al [21] studied the default risk contagionin banking systems under two different network structuresand pointed out the default risk contagion is much severerunder the random network than the endogenous networkGeorg et al [22 23] proposed an interbank network systemthat introduced the central bank as the lender of last resortand demonstrated that the money-center network is moreresilient than the random network Meanwhile there is agrowing body of research on the empirical analysis of thenetwork structure of the interbank network Soramaki et al[24] studied the interbank debt connection in Fedwire andfound that the interbank network in the United States hasthe characteristics of a small-world network When ana-lyzing the CHAPS of British Becher et al [25] pointed outthat the path length of the British interbank network is closeto that of the United States and the British interbanknetwork is also a small-world network Souma et al [26]discovered that the interbank network in Japan has scale-freestructure characteristics Edson and Cont [27] observed thatthe nodes of the Brazilian interbank network obey a power-law distribution and belong to a scale-free network Iori et al[28] found through researching the Italian real interbanklending data that the Italian interbank market networkpresents a random network structure Sumer and Ozyıldırım[29] used exposure data on the Turkish banking system tostudy the interbank network structure and showed that thecore-peripheral structure centered on highly liquid largebanks is the main interbank network structure

Indeed as the existing literature has highlighted theinterbank market is an important factor affecting the sta-bility of the banking system However from the bubble andcollapse of the financial market the shadow banking hasundergone a major dysfunction before and after the crisis+is change made shadow banking to be regarded as aninternational systemic risk transmitter and the importantfactor that undermines financial stability in times of crisis+e term shadow banking was coined byMcCulley [30] andwas picked up by policymakers [31] According to theFinancial Stability Board (FSB) [32] shadow banking is thecredit intermediation that channels funding from deposi-tors to investors through a range of securitization andsecured funding techniques and may cause systemic fi-nancial risks and regulatory arbitrage risks Althoughshadow banks conduct credit and maturity transformationsimilar to that of traditional banks shadow banks are es-sentially fragile Adrian and Ashcraft [33] pointed out thatunlike traditional banks under the policy safety net thefunds of depositors in shadow banks are not protectedPozsar et al [34] compared the size of shadow bankingduring the crisis and found that before the crisis the size ofshadow banking showed a sudden growth trend andreached a peak Bernanke et al [35] discussed that shadowbanks use maturity transformation to avoid risks butfragile assets and liabilities caused shadow banks to collapseexcessively during the crisis and systemic risks increaseddramatically By documenting the performance of shadowbanking Wiggers and Ashcraft [36] observed that shadowbanks defaulted in large numbers in times of crisis whichdestroyed the banking system stability Nevertheless Ross[37] Allen and Gale [38] stressed that the financing ex-pansion of shadow banking is in line with Paretorsquos optimalimprovement which can share part of the systemic risk andmaintain the stability of the banking system Colombo et al[39] constructed a shadow banking model and emphasizedthat the form of propagation after the crisis shock wouldreduce the system to resist risks and the correspondingstability level of the banking system An improved shadowbanking model is proposed by Gennaioli et al [40] and theresults showed that investors ignore tail risk which couldmake the banking system vulnerable to crisis shocks butunder rational expectation shadow banking would help toresist systemic risk and maintain system stability Moreiraand Savov [41] built a macro-finance model of shadowbanking and argued that shadow banking expands the li-quidity provision as well as builds up the fragility of thesystem Elgin and Oztunali [42] noted through a two-sectordynamic general equilibrium model that the relative size ofshadow banking will influence the banking systemrsquos sta-bility Besides Irani et al [43] investigated the connectionsbetween bank capital regulation and the lightly regulatedshadow banks Loayza et al [44] and Elias [45] qualitativelyanalyzed the effect of shadow banking on the bankingsystemrsquos stability from the perspective of the labor marketand the money market fund respectively

Previous research on the impact of shadow banking onthe banking systemrsquos stability has been carried out from theaspects of qualitative analysis related to changes in shadow

2 Discrete Dynamics in Nature and Society

banksrsquo characteristics and static analysis based on simplemodels However it did not consider the complex rela-tionship between banks that is the complex interbanknetwork and failed to reveal the changes in the stability ofthe banking system with shadow banking under the dynamicevolution mechanism As pointed out by the existing re-search the complex interbank network not just presents asingle network structure but also can be built as a variety ofnetwork structures Different interbank networks havedifferent abilities to contagion and resist risk It is verymeaningful to identify which interbank network used toconstruct the banking system with shadow banking candisperse and absorb risk more efficiently To the best of ourknowledge there is no quantitative research on the impact ofthe sensitivity of different network structures on the stabilityof the banking system with shadow banking by proposing avariety of interbank network structures Given the aboveproblems to explore the stability of the banking system withshadow banking more comprehensively and get rid of thelimitation of the single interbank network structure basedon the complex network theory and the dynamic evolutionof bank balance sheet random network small-world net-work and scale-free network are respectively used to buildthe dynamic complex interbank networkmodel with shadowbanking +en the sensitivity and difference of the bankingsystem with shadow banking under various networkstructures are compared and analyzed

Unlike our previous research on the stability of thebanking system with shadow banking under macroeco-nomic fluctuation [46] although the same model of thebanking system with shadow banking is used in this paperhowever the interbank network structures are different +econtribution of this paper is that it is the first quantitativeinvestigation into the impact of different interbank networkstructures on the stability of the dynamically evolvingbanking system with shadow banking Compared with thecurrent qualitative and static research our paper fullyconsiders the complex relationships between banks and thevarious connections that is the diversity characteristic ofthe interbank network structure and proposes a dynamicinterbank network model under different network structuresto effectively simulate the dynamic operation and evolutionof the banking system +is enables us to observe thechanging trend of systemic risk under various interbanknetworks compare and analyze which interbank networkstructure has a better ability to resist risk thereby providingmore valuable reference results for regulators and policy-makers +e remainder of this paper is organized as followsAfter this introduction Section 2 describes the dynamiccomplex interbank network model with shadow bankingunder different interbank networks Section 3 presents themain results and Section 4 provides a conclusion

2 The Model

A dynamic complex interbank network model under dif-ferent interbank networks for the banking system withshadow banking is constructed in this paper+e structure ofthe banking system with shadow banking is shown in

Figure 1 +e model takes into account the impact of dif-ferent interbank network structures (the random networkthe small-world network and the scale-free network) thedynamic evolution of the bank balance sheet and the centralbank as the liquidator and supporter on the stability of thebanking system with shadow banking

21 Interbank Network Structures +e interbank network isa complex network with multiple characteristics Hence toexplore the stability of the banking system with shadowbanking as comprehensively as possible we use the randomnetwork the small-world network and the scale-free net-work respectively to build the interbank network of thebanking system as shown in Figure 1(a) +e nodes rep-resent the banks and the edges between the nodes representthe interbank credit lending relationship Apart from thecentral bank there are G bank nodes in the banking systemamong which the number of traditional bank nodes is U andthe number of shadow bank nodes is V that is GU+V Atany time there a finite number of functioning banks Dif-ferent interbank network structures may have differentinfluences on the risk contagion

Inspired by Iori et al [15] Nier et al [16] and Georg[23] we first establish the interbank lending network basedon the random network +e interbank credit lending re-lationship is represented by a binary matrix X where Xij 1or Xij 0 Xij 1 shows that there is a credit connectionbetween bank i and bank j and Xij 0 indicates there is nocredit connection At each time t a bank connects to anyother bank with the probability cij (0le cij le 1) which formsa new random network of potential interbank lending re-lationships +e independent and opacity characteristics ofshadow banks should be noted [47] therefore no creditconnection between shadow banks is constructed as shownin Figure 1

Next referring to the work of Watts et al [48] we proposethe interbank lending network based on a small-world networkFirstly there are G banks and a one-dimensional interbanknetwork with K nearest neighbors for each bank is formed inwhich there is no coupling relationship between shadow banks+en at each time t randomly reconnect one of the endpointsof each edge with the probability p When reconnecting itshould not only ensure that there is no self-loop and doubleedge but also ensure that there is no connection betweenshadow banks

We also establish the interbank lending network basedon the scale-free network referring to Barabasi et al [49]Starting from the interbank network with m0 independentbank a new bank with m edges is introduced at each time twhere m0 gem Simultaneously the probability πi of the newbank i connected to the old bank j has a relationship with thedegree ki and kj of the bank i and bank j respectively that isπi ki1113936 kj +ere is no connection between shadow banks

22)e Banking Systemwith Shadow Banking Based on theresearch of Pan and Fan [46] the banking system withshadow banking is constructed in this paper Traditionalbanks shadow banks and the central bank are included in

Discrete Dynamics in Nature and Society 3

the proposed model +e behaviours of each bank are de-scribed by the bank balance sheet Different from previousstudies the bank balance sheet in this paper is dynamicallyevolved over time As shown in Figure 1(b) the asset in thebank balance sheet is composed of the liquidity L and in-vestment I and the liability consists of deposit A interbanklending B and ownerrsquos equity E +e initial bank balancesheet of bank i is described as follows

Li(t minus 1) Ai(t minus 1) + Bi(t minus 1) + Ei(t minus 1)

minus 1113944τ

k1Ii(t minus k)

(1)

where Li(t minus 1) is the liquidity of bank i at time t minus 1 Ai(t minus

1) and Ei(t minus 1) are the deposit and the ownerrsquos equity ofbank i at time t minus 1 respectively 1113936

τk1 Ii(t minus k) is the total

investment of bank i in τ investment periods Bi(t minus 1)

1113936Gk1 bij(t minus 1) is the total interbank lending amount of bank

i at time t minus 1 At time t minus 1 bij(t minus 1)gt 0 denotes theamount borrowed by bank i from bank j bij(t minus 1)lt 0means bank i lends to bank j that is bij(t minus 1)

minus bji(t minus 1) bij(t minus 1) minus bji(t minus 1) 0 shows that there isno lending relationship between banks

+e operation of the banking system with shadowbanking is regarded to be in discrete time which is denotedby t t 0 1 2 T It is assumed that interbank lendingbetween banks within the system only relies on the latestbank balance sheet At time t the balance sheet of bank i isupdated to

Li(t) Li(t minus 1) + Ai(t) minus Ai(t minus 1)( 1113857 minus raAi(t minus 1)

+ ρ 1113944τ

k1Ii(t minus k) + Ii(t minus τ)

(2)

whereraAi(t minus 1) is the interest paid by the banki todepositorsra is the deposit interest rate (for simplicity weuse the same terminology ldquodepositsrdquo to represent depositsfor traditional banks and funding for shadow banks) InpracticeAi(t) |A + AδAεt| whereA is the mean of randomdeposits of all banks AδA is the standard deviation ofrandom deposits of all banks and εt sim N(01) ρ1113936

τk1 Ii(t minus

k) and Ii(t minus τ) are the income of bank i from the investmentand the expiry investment respectively τ is the investmentcycle ρ is the return on investment of each period +ereturn on investment ρ can be expressed as

ρ 0 1 minus q

ρ q1113896 (3)

where q is the investment recovery probability After bank i

receives the investment profit it may carry on the dividendand reinvestment +e dividend and reinvestment of tra-ditional banks refer to the model of Iori et al [15] and is notrepeated here +is paper mainly describes the businessactivities of shadow banks At time t the dividend of shadowbank i satisfies the following conditions

Di(t) max 0 min θ ρ 1113944τ

k1Ii(t minus k) minus raAi(minus 1)⎛⎝ ⎞⎠ Li(t)⎡⎢⎢⎣ ⎤⎥⎥⎦⎡⎢⎢⎣

(4)

Shadowbank 1

Traditionalbank 1

Traditionalbank 2

Traditionalbank U

Shadowbank 2

Shadowbank 3

Shadowbank V

Balance sheet

LiquidityLi (t)

Deposit Ai (t)Interbank lending

Bi (t)

Ownerrsquo s equityEi (t)

InvestmentIi (t)

Central bank

(b)

(c)

(a)

Random Small world Scale free

Figure 1 +e structure of the banking system with shadow banking under various interbank networks


where θ is the deposit ratio of shadow banks After thedividend is paid shadow banks need to invest the remainingliquidity fund to improve their profits +e investment Ii(t)

of shadow bank i at time t can be decided by the followingequation

Ii(t) min max 0 Li(t) minus Di(t)1113858 1113859ωi(t)1113858 1113859 (5)

where ωi(t) is the investment opportunity of shadow bank i

at time t which is defined as ωi(t) |ω + ωδφηt| ω is themean value of all shadow banksrsquo investment opportunitiesωδφis the standard deviation of all shadow banksrsquo investmentopportunities and ηt obeys the normal distribution N(0 1)

After dividends and investments if a bank i still hasample liquidity Li(t)ge 0 the banki is a potential creditorbank which can provide funds in the interbank marketConversely if banki lacks liquidity Li(t)lt 0 it is a debtorbank it needs to borrow from the interbank market in orderto maintain its normal operation When the lending fromthe interbank market is sufficient to repay the previous loanthe debtor bank can continue its operation If the debtorbank fails to borrow enough money from the interbankmarket to repay its arrears and deposit interest it will belabelled as a member of the default set D and wait for centralbank clearance or support as shown in Figure 1(c)

+e operations of traditional banks are supervised by thecentral bank while the activities of shadow banks are freefrom the scope of the central bank regulation [31] So onlytraditional banks can receive support from the central bankAt timet the assistance of the central bank to the traditionalbank i is

Hi(t) Ri(t) minus Li(t) Ri(t)gtLi(t)

0 otherwise1113896 (6)

where Ri(t) βAi(t) is the legal deposit reserve required bytraditional bank i at time t the deposit reserve ratio is βWhen Ri(t)gt Li(t) Ri(t) minus Li(t) is the assistance of thecentral bank to the traditional bank i Meanwhile the li-quidity and debts of the assisted traditional bank i both turnto 0 (Bi(t) 0 and Li(t) 0) the traditional bank i goes out ofthe default set D and rejoins into the operation of thebanking system Otherwise the traditional bank i pays legaldeposit reserve by itself and continues to operate When theilliquid bank i is a shadow bank it is cleared by the centralbank and shadow bank irsquos debts are paid proportionally [50]+e debt repayment is calculated as follows

Cij(t)

Ei(t)lowastbij(t)

1113936fj1 bij(t)

if bij(t)gt 0 andEi(t)gt 0

0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)

where Ei(t) represents the ownerrsquos equity of the shadowbank i bij(t) is the interbank borrowing amount betweenthe shadow bank i and traditional bank j and 1113936

fj1 bij(t) is

the total amount of the shadow bank i borrowed from nomore thanf traditional banks (f is the maximumnumber of

traditional banks that can be borrowed by a shadow bank)+en the debts of shadow banki update to 0 (Bi(t) 0) andit remains a member of default set D for all subsequent time

23 Dynamic Update Algorithm +e dynamic update al-gorithm is rendered to determine how the banking systemwith shadow banking evolves from one state to another +ealgorithm is divided into 4 steps that are briefly described asfollows

(i) Step 1 determine and build the interbank networkRandom network small-world network or scale-free network is constructed according to the de-mand and the corresponding initial parameters andvariables are respectively set

(ii) Step 2 update the liquidity of the bank and then thedividend and investment According to (2) the li-quidity of the bank i is calculated at time t If thebank i with sufficient liquidity (Li(t) ge 0) it carriesout dividend distribution Di(t) and investmentIi(t) according to (4) and (5) If the bank i withliquidity shortage (Li(t) lt 0) it will go for interbanklending

(iii) Step 3 interbank lending in the system Afterdividend Di(t) and investment Ii(t) are operatedthe liquidity of bank i updates toLi(t) Li(t) minus Di(t) minus Ii(t) If the liquidity ofbanki is positive bank i is a creditor bank whichcan lend its liquidity to illiquid banks Otherwisethe bank i is a debtor bank that needs to borrowfrom flush liquidity banks to pay its loans Aftercreditor banks and debtor banks are determinedinterbank lending activities begin If the debtorbank i can borrow sufficient funds from thecreditor banks to repay the previous loan andinterest ie Li(t) minus (1 + rb)Bi(t minus 1)ge 0 (rb is theinterbank market interest rate) it can continue tooperate if the debt bank i cannot borrow sufficientfunds to repay the previous loan and interest ieLi(t) minus (1 + rb)Bi(t minus 1)lt 0 it becomes a memberof the default set D and is then supported orcleared by the central bank

(iv) Step 4 supported or cleared by the central bank Attime t if the default bank i is a traditional bank it isaided by the central bank according to (6) thencomes out of the default set D and continues toevolve in the system If the default bank i is a shadowbank it is cleared by the central bank according to(7) and then remains a member of default set D forall subsequent time +e aided or cleared bank irsquosliquidity and debts are both updated to 0 ieLi(t) 0 and Bi(t) 0

3 Simulation and Analysis

31ModelParameters To conduct the simulation analysis ofthe above model firstly it is necessary to give the values ofmodel parameters +e maximum simulation time step is set


to 100 (within 100 time steps the dynamic characteristics ofthe banking system network can be fully embodied) andreferring to the studies of Iori et al [15]Watts et al [47] andBarabasi [48] as well the actual banking system the pa-rameters are set in Table 1

+e systemic risk of the banking network system at time t

is determined by the internal state and parameters of thenetwork system In order to effectively depict the systemicrisk of the banking network system the average number ofdefault banks in [t+1 t+W] time range is the normalizedvalue R(t)R(t) Can be calculated as follows

R(t) 1

WOe

1113944

Oe

i11113944

t+W

jt+1

Yij

Yij + Z

ij

(8)

where W is the time interval and the average proportion ofdefault bank in the future W time can indicate the systemicrisk of the system at a certain moment W is set toW 10 inthis paper Oe is the time number of the simulation Yi

j andZi

j is the number of default bank and survival bank at time j

in the ith simulation respectively According to the study ofCaccioli et al [51] more than 5 of bank failures in thebanking network system consider that risk contagion occursthat is risk contagion occurs in a wider range of crisisphenomena +erefore given the parameters assuming thatthe total number of experiments is n and the number of riskcontagion is n1 the average probability of risk contagion(PC) in the banking system is

PC n1

n (9)

Record the number of default banks at the ith riskcontagion occurs as ni

2 then the average degree of riskcontagion (DC) is expressed as follows

DC 1113936

n1i1 n

i2G1113872 1113873

n1 (10)

Intuitively R(t) reflects the dynamic change of systemicrisk of the banking network with timePC and DC analyzethe risk contagion in the banking network system from theperspective of statistics +e comprehensive application ofR(t) PC and DC carry out a more complete risk analysis onthe banking network system with shadow banking

4 Results

+e evolutionary process of a bank under three interbanknetworks is shown in Figure 2 +e liquidity ownerrsquos eq-uity investment and dividend of banks are all dynamicchanges +e banking system evolves over time In theevolutionary process of the banking network some bankswill go bankrupt and lead to the chain bankruptcy of otherbanks in the same network As shown in Figure 2(a) underthe random network the bank ownerrsquos equity increasesthrough continuous investment income and the liquidity isrelatively stable However at the end of the networkevolution the bank investment has shrunk assets havebeen damaged the ownerrsquos equity has fallen to a negative

value liquidity is insufficient and eventually results inbankruptcy Figures 2(b) and 2(c) respectively show theevolution of a bank under the small-world network andscale-free network Unlike the random network the time ofsignificant change in bank liquidity ownerrsquos equity in-vestment and the dividend of the small-world network andscale-free network are advanced +is shows that a bankrsquosfailure may be caused by two aspects On the one hand thebankrsquos own poor business strategy makes its income in-sufficient to pay its deposit interest and loans leadingultimately to bankruptcy On the other hand when a bankin the system fails due to improper operation it will quicklyinfect other banks through the interbank network resultingin a large number of insolvent banks a huge decline inliquidity and reduced risk resistance Different interbanknetworks have different contagion ability It can be foundfrom above that the circumstance of a bank is not onlyrelated to its own investment strategy but is also closelyrelated to the interbank network structure

Figure 3 shows the changes in the survival ratio with timeunder three interbank networks and the correspondingsystemic risk It can be seen from Figure 3(a) that under anykind of interbank network structure bank default occurs inthe system in the first step and the bank survival rate beginsto decline +is is due to the different initial state and op-eration strategies of each bank in the banking systemHowever unlike the slow decline of the bank survival rate ofthe random network the bank survival rate of the small-world network and the scale-free network have undergonesignificant declines at around 30 steps and 40 steps re-spectively until it was maintained at a low level +e

Table 1 Benchmark parameter of the model

Parameter Description Benchmarkvalue

G +e total number of banks 400U +e number of traditional banks 100V +e number of shadow banks 300c Connection probability 003K Nearest neighbours for each bank 2

pProbability of reconnect one

endpoints of each edge 002

m0Number of independent banks

started 50

m Edges of a new bank 2

f

+e maximum number of traditionalbanks that can be borrowed by a

shadow bank3

I Initial investment 500τ Investment periods 3θ Deposit ratio 03ω Average investment opportunities 500ρ Return on investment (ROI) 0045q Investment recovery probability 085δφ Investment volatility 035A Average deposit 1000δA Deposit volatility 025ra Deposit interest rate 0004rb Interbank market interest rate 0008β Deposit reserve ratio 035


corresponding systemic risk Figure 3(b) shows that thebanking system based on the small-world network has thelargest degree of systemic risk followed by the scale-freenetwork and its systemic risk has decreased +e bankingsystem under the random network has always been relativelystable and has a low level of systemic risk Obviously fromthis different interbank network structures will transmitdifferent levels of systemic risk +is is due to banksestablishing direct or indirect linkage through differentinterbank network structures +e random network ran-domly connects the banks and the dispersed networkstructure can avoid the excessive concentration of riskreduce the cumulative effect of risk prevent the occurrenceof bank default and maintain the stability of the systemWhile under the small-world and the scale-free networkstructure the linkage between banks is relatively close If onebank bankrupts it will easily lead to a domino effect ofbankruptcy due to insolvency and lack of liquidity

accelerate the spread of contagion in the small-world net-work and the scale-free network and then detonate systemicrisk

In the real financial system the return on investmentrepresents the overall situation of the current financialmarket +erefore we analyze the impact of ROI change onthe systemic risk of the banking systemwith shadow bankingunder different interbank networks Figures 4(a)ndash4(c) showthe systemic risk with different ROI under different inter-bank networks From Figures 4(a)ndash4(c) it can be seen thatunder the same ROI the systemic risk of the randomnetwork is always lower than that of the small-world net-work and the scale-free network With the increase in ROIthe outbreak time of systemic risk in the banking network isdelayed and the level of systemic risk declines Among thethree network structures the systemic risk level of therandom network and the scale-free network decreases sig-nificantly with the increase in ROI For the small-world

0 20 40 60 80Timestep

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

Random

LiquidityOwnerrsquosequity

InvestmentDividend

(a)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

0 20 40 60 80Timestep

Small-world


InvestmentDividend

(b)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney


InvestmentDividend

0 20 40 60 80Timestep

Scale-free

(c)

Figure 2 +e evolutionary process of a bank under diverse interbank networks

0 20 40 60 80Timestep

02

04

06

08

1

Surv

ival

ratio

RandomScale-freeSmall-world

(a)


0 20 40 60 80Timestep

0

02

04

06

08Sy

stem

ic ri

sk

(b)

Figure 3 (a) Changes in the survival ratio of diverse interbank networks (b) Dynamic changes in systemic risk of diverse interbanknetworks


network although the time of systemic risk outbreakgradually pushed from 20 steps to 40 steps as the ROI in-creases the overall risk level decreases slowly and insig-nificantly +e explanation is that by increasing the ROI asufficient spread between the ROI and the deposit interestrate will be generated increasing the overall profitability ofthe bank which protects banks from illiquidity Meanwhiledifferent interbank network structures determine differentinterbank lending relationships which in turn determine theliquidity situation of the banking system and affect thestability of the banking system Figures 4(d) and 4(e) are theaverage probability of risk contagion and the average degreeof risk contagion of different interbank networks underdifferent ROI Figure 4(d) shows that when the ROI is smallthe average probability of risk contagion of three networks isgreater than 60 When the ROI increases the averageprobability of risk contagion of the random network dropssharply and drops to 0 when the ROI is 0045 +e averageprobability of risk contagion of the scale-free network de-creases when the ROI exceeds 0055 Only the averageprobability of risk contagion of the small-world networkremains at a high level It can be observed from Figure 4(e)that the average degree of risk contagion of the three net-works all show a downward trend but the average degree of

risk contagion of the small-world network and the scale-freenetwork is always higher than that of the random networkWhen the ROI is greater than 0035 the average degree ofrisk contagion of the random network and the scale-freenetwork decline obviously compared with the small-worldnetwork When the ROI increased to 0045 the averagedegree of risk contagion of the random network decreases to0 and there is no systemic risk in the banking system withshadow banking under the random network When the ROIis 0065 the average degree of risk contagion of the scale-freenetwork is less than 20 and the systemic risk level reducesbut the small-world network still has a large average degreeof risk contagion +e above results show that ROI changehas an impact on the stability of the banking system withshadow banking +e sensitivity of different networkstructures to ROI change is different +e effect on in-creasing ROI is more significant under the random networkwhich results in a lower contagion risk because borrowerscan get enough liquidity In contrast the effect on increasingROI is weak under the small-world network and the scale-free network because the relatively centralized networkstructures make lenders overlap and results in limited li-quidity available to borrowers +erefore the random net-work has a better resilience to risk

0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)

Figure 4 Evolution results of the diverse interbank networks under different ROI


In addition to ROI the choice of bank investmentstrategy has a vital effect on the bank operation andmaintaining the banking system stability In the financialmarket different investment products generally have dif-ferent investment periods +e length of the investmentperiod determines whether the liquidity of the bank issufficient and thus determines the survival of the bank+erefore the reasonable choice of investment periods playsa key role in bank risk control Figures 5(a)ndash5(c) respec-tively show the systemic risk evolution results of differentinvestment periods under different interbank networksWhen the investment period is 2 the systemic risk of thebanking system with shadow banking decreases from thesmall-world network to the scale-free network and then tothe random network+e systemic risk value under the threenetworks is low and less than 15 and the banking systemis in a stable state When the investment period extends to 4and 6 the systemic risk begins to break out +e small-worldnetwork and the scale-free network almost simultaneouslyerupt with systemic risk and the time of systemic riskoutbreak of the random network also advances with theextension of the investment periods +is is because with theextension of the investment period the level of liquidity inthe banking system decreases Banks that cannot recovertheir investment and cannot obtain sufficient funds to repaytheir debts through interbank lending default and then therisk is transmitted to more banks through the interbanknetwork which induces the systemic risk outbreak and thestability of the banking system is damaged Figures 5(d) and5(e) depict the average probability of risk contagion and theaverage degree of risk contagion of different investmentperiods under the three networks We find that the averageprobability of risk contagion of the three networks increaseswith the extension of the investment period When theinvestment period is greater than or equal to 4 the averageprobability of risk contagion under the three networks ismore than 85 Meanwhile with the investment periodfrom 2 to 6 the average degree of risk contagion of the threenetworks also gradually increased+e above results indicatethat the three interbank networks are all sensitive to thechange of the investment period and an increase in theinvestment period produces an increase of systemic risk Tobe specific the long investment period will result in thedecrease of the available liquidity scale in the system In theprocess of interbank lending borrowers are unlikely to getenough amount and lenders may also default due to therisky loans which lead to the decline in the bankrsquos survivalrate and accumulates the systemic risk +erefore setting areasonable investment period is particularly essential forprotecting the stability of the banking system with shadowbanking

Deposit is a necessary part of the bank balance sheet andthe main source of funds +e spread between investmentand deposit earns a bankrsquos profit +erefore the profitabilityof the bank is affected by the deposit Affected by macro-economic fluctuations the deposit of the bank alwayschanges Figure 6 describes the systemic risk evolution re-sults of different average deposits under the three interbanknetworks As shown in Figures 6(a)ndash6(c) the systemic risk of

the three interbank networks all decreases with the increaseof the average deposit When the average deposit is 750 thethree interbank networks have high systemic risk and thesmall-world network has the highest systemic riskWhen theaverage deposit is 1150 the systemic risk of the small-worldnetwork and the scale-free network decline significantly andthe systemic risk of the random network disappears +ereason is that the increase in the average deposit provides thebank with sufficient capital increases liquidity and reducessystemic risk +erefore the increase in the average depositcan improve the stability of the banking system with shadowbanking Figures 6(d) and 6(e) show the average probabilityof risk contagion and the average degree of risk contagion ofdifferent average deposits under the three networks Whenthe average deposit is less than or equal to 850 the small-world network and the scale-free network have a high andalmost the same average probability of risk contagion andthe average degree of risk contagion is also at a high value Asthe average deposit increases from 850 to 1150 the averageprobability of risk contagion and the average degree of riskcontagion of three networks are gradually decreased and theaverage probability of risk and the average degree of riskcontagion of the random network change to 0 when theaverage deposit is 1150 +e above results show that thechange in the average deposit has a significant impact on thestability of the banking system with shadow banking +ehigher average deposit results in a lower risk of insolvencyand a wider range of liquidity fluctuation Meanwhile itindicates that different interbank networks have differentelastic responses to resist systemic risk under the change ofaverage deposit Compared with the small-world networkand the scale-free network the random network enables amore balanced distribution of liquidity guarantees thesuccessful progress of interbank lending and has a strongability to resist systemic risk

It is one of the necessary business activities for banks topay deposit interest to depositors on schedule Deposit in-terest is the main expenditure of banks so the fluctuation ofdeposit interest rate will affect the liquidity of banks Figure 7gives the evolution results of the diverse interbank networksunder different deposit interest rates As shown inFigures 7(a)ndash7(c) with the increase of the deposit interestrate the systemic risk of the three networks has all changedIn the process of the deposit interest rate changing from0003 to 0005 the systemic risk of the random network andthe scale-free network gradually increased and the systemicrisk of the small-world fluctuates at a high level +e timingof the outbreak of systemic risk in three interbank networksadvances with the increase in the deposit interest rate +ispoints out that the interbank network is sensitive to thechange of the deposit interest rate which could impact thestability of the banking system to a certain extentFigures 7(d) and 7(e) show that when the deposit interestrate changes from 0003 to 0004 the average probability ofrisk contagion of three networks increases while the vari-ation range of the average probability of risk contagion isrelatively small in other deposit interest rates +is con-clusion enlightens us there is a deposit interest rate valuewith maximum contagion ability for the interbank networks


When the deposit interest rate reaches this value the bur-dens of the debtor banks aggravate the risk of insolvencyincreases and thus there is a great shock on the bankingnetwork which destroys the stability of the banking systemMeanwhile among the three interbank networks the riskcontagion probability and risk contagion degree under thesmall-world network is much higher than that of the randomnetwork because a more centralized interbank network isoften more fragile [16] much more banks default due toilliquidity or insolvency and can neither borrow nor lend inthe interbank network

Shadow banking is one of the main factors that inducefinancial crises +erefore in addition to the operationalactivities of banks the density of shadow banking in thesystem also has an essential impact on the banking system+is paper defines the density of shadow banking d as theratio of the number of shadow banks V to the total numberof banks G in the network that is d VG Figure 8 showsthe evolution results of the diverse interbank networks underdifferent densities of shadow banking In Figure 8(a) thesystemic risk of the three networks is less than 25when thedensity of shadow banking is 02 and the systemic risk of thesmall-world network and the scale-free network decrease

with time+is shows that an appropriate amount of shadowbanks can share the systemic risk and maintain the stabilityof the banking system However Figures 8(b) and 8(c) showthat with the increase of the density of shadow banking thesystemic risk of the three interbank networks increasesAmong them the systemic risk of the small-world networkand the scale-free network increases significantly which dueto the small-world network and the scale-free network aremore concentrated than the random network so the spreadof risk is faster and wider Figures 8(d) and 8(e) show thecontagion probability and contagion degree of risk in threenetworks under the different density of shadow banking+eaverage probability of risk contagion of the small-worldnetwork and scale-free network increases significantly withthe rise of the density of shadow banking+e average degreeof risk contagion of the small-world network and the scale-free network also obviously go up when the density ofshadow banking is greater than or equal to 04 +e ex-perimental results show that the density of shadow bankingis a crucial factor affecting the stability of the bankingsystem+e explanation is that unregulated shadow bankingnot only promotes interbank lending activities but alsoaccumulates the fragility of the banking system+e increase

0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)

Figure 5 Evolution results of the diverse interbank networks under different τ


of the density of shadow banking intensifies the accumu-lation of the systemic risk once a bank defaults there willimmediately be an outbreak of the systemic risk Influencedby the network structures in face of the change in the densityof shadow banking the small-world network and the scale-free network are easier to accumulate and spread systemicrisk while the random network has a better ability to dis-perse and absorb risk

Finally we analyze the changes in the systemic risk of thebanking system under three interbank networks when thebanking system suffers from asset loss +e impact on thebanking system is not only caused by the business activitiesof banks during a financial crisis the instantaneous assetdevaluation also causes huge losses to a banksrsquo assets whichwill lead to serious damage to the stability of the bankingsystem Figure 9 shows the systemic risk evolution of dif-ferent interbank networks that suffered a loss in assets at t

20 As shown in Figures 9(a)ndash9(c) when the interbanknetworks are shocked by a loss in assets the bank defaultcaused by funds shortage will rapidly occur in the small-world network and the scale-free network +e risk of bankdefault spreads rapidly through the centralized interbanknetwork which leads to the chain failure reaction of banksand the outbreak of systemic risk With the increase of a loss

in the asset from 15 to 45 the risk of the small-worldnetwork and the scale-free network is expanding in a shortperiod of time the outbreak time of systemic risk is con-stantly advanced the peak value of systemic risk is alsoincreasing and the stability of the banking system is seri-ously damaged However the random network shows adelayed response to the shock of the asset loss When the lossin the asset of the banking system is 15 and 30 bankdefault does not appear immediately in the random networkas part of the risk is absorbed by the random network +elevel of systemic risk is significantly lower than that of thesmall-world network and the scale-free network But whenthe asset loss reaches 45 the excessive shock of the assetloss has broken through the ability of the random network toresist risk and leads to a large number of bank credit de-faults the systemic risk outbreak and the banking systemcollapse +e above results show that the larger size of theasset loss shock brings about a higher risk of illiquidityBesides the interbank network structure has an importanteffect on the resistance and contagion of risk +e riskcontagion caused by bank illiquidity quickly happens in therelatively centralized small-world network and the scale-freenetwork +e random network generates a dispersed net-work structure which provides more chance for interbank

0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)

Figure 6 Evolution results of the diverse interbank networks under different A


0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)

Figure 7 Evolution results of the diverse interbank networks under different ra

0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued


lending and absorbs part of the risk But it should be notedthat the interbank network will lose the ability to protect thestability of the banking system if the shock of the asset loss istoo extensive

5 Conclusions

From the perspective of the stability of the financial systemnot only interbank market structure but also shadowbanking affects the stability of the financial system Howeverthe current research on the impact of shadow banking on thestability of the banking system did not consider the complexrelationship between banks and failed to reveal the changesof the stability of the banking system under the dynamicevolution mechanism of shadow banking In order to ex-plore the stability of the banking system with shadowbanking more comprehensively based on the complexnetwork theory and the dynamic evolution of the bankbalance sheet the random network the small-world

network and the scale-free network were used to establishthe dynamic complex interbank networkmodel with shadowbanking in this paper +rough the proposed model thesensitivity and difference of the banking system with shadowbanking under various network structures were comparedand analyzed A series of conclusions are as follows

(i) Different interbank network structures have dif-ferent abilities to contagion and resist the systemicrisk of the banking system with shadow bankingWith the relatively centralized interbank networkit is easier to increase the contagion probability andcontagion degree of risk Generally the system riskis severer under the small-world network and thescale-free network than the random network

(ii) Changes in ROI have an impact on the stability ofthe banking system with shadow banking +egreater the ROI the more stable the banking systemwith shadow banking+e resilience of the different

02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)

Figure 8 Evolution results of the diverse interbank networks under different d

0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)

Figure 9 Evolution results of the diverse interbank networks suffer a loss at step 20


interbank networks to the changes in ROI is dif-ferent and the resilience of the random network isbetter than that of the small-world network andscale-free network

(iii) +e banking system with shadow banking is verysensitive to changes in the investment periods+e extension of the investment period signifi-cantly increases the systemic risk of the bankingsystem +e random network the small-worldnetwork and the scale-free network are all sen-sitive to the change in the investment period It isvery essential to set a reasonable investmentperiod for banks to maintain the stability of thebanking system

(iv) +e increase in the average deposit of banks canimprove the stability of the banking system withshadow banking Under the changes in the averagedeposit of banks the random network has a betterability to resist risks than the small-world networkand the scale-free network

(v) +e increased deposit interest rate reduces the li-quidity of banks and promotes the systemic risk of thebanking system +ere is a deposit interest rate valuewith maximum contagion ability for the interbanknetworks and it has a great shock on the stability ofthe banking system Among the three interbanknetworks the risk contagion probability and riskcontagion degree of the small-world network is thehighest while that of the random network is thelowest

(vi) +e greater the density of shadow banking the higherthe contagion probability and contagion degree of riskin the system +e shadow banking density is animportant factor affecting the stability of the bankingsystem with shadow banking Facing a change in thedensity of shadow banking the small-world networkand the scale-free network easily accumulate systemicrisk while the random network has a better ability todisperse and absorb risk

(vii) When the banking system with shadow banking isaffected by the loss in assets comparedwith the small-world network and the scale-free network the ran-domnetwork has better ability to resist and absorb therisk However the shock of excessive loss in assets willdirectly break through the protection of the banknetwork detonate systemic risk and destroy thestability of the banking system with shadow banking

+is paper provides a scheme for quantitatively inves-tigating the impact of different interbank network structureson the stability of the banking system with shadow bankingMeanwhile it gives a reference for policymakers and reg-ulatory authorities to prevent systemic risk introduced byshadow banking +e dynamic evolution interbank networkmodel proposed in this paper provides a basic framework forthe study of the systemic risk of shadow banking In thefuture the actual data can be used to make an empiricalanalysis based on this framework

Data Availability

+e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

+e authors declare no conflicts of interest

Acknowledgments

+is work was supported by the National Natural ScienceFoundation of China (Grant No 71971054) and the ShanghaiNatural Science Foundation (Grant No19ZR1402100)

References

[1] C M Kahn and J Santos ldquoEndogenous financial fragility andprudential regulationrdquo SSRN eLibrary vol 10 2005

[2] J F Cocco F J Gomes and N C Martins ldquoLending rela-tionships in the interbank marketrdquo Journal of Financial In-termediation vol 18 no 1 pp 24ndash48 2009

[3] H S Shin ldquoRisk and liquidity in a system contextrdquo Journal ofFinancial Intermediation vol 17 no 3 pp 315ndash329 2008

[4] R Cifuentes G Ferrucci and H S Shin ldquoLiquidity risk andcontagionrdquo Journal of the European Economic Associationvol 3 no 2-3 pp 556ndash566 2005

[5] A Temizsoy G Iori and G Montes-Rojas ldquo+e role of bankrelationships in the interbank marketrdquo Journal of EconomicDynamics and Control vol 59 pp 118ndash141 2015

[6] F Castiglionesi ldquoFinancial contagion and the role of thecentral bankrdquo Journal of Banking amp Finance vol 31 no 1pp 81ndash101 2007

[7] A Hasman and M Samartın ldquoInformation acquisition andfinancial contagionrdquo Journal of Banking amp Finance vol 32no 10 pp 2136ndash2147 2008

[8] M Kanno ldquoAssessing systemic risk using interbank exposuresin the global banking systemrdquo Journal of Financial Stabilityvol 20 pp 105ndash130 2015

[9] W Silva H Kimura and V A Sobreiro ldquoAn analysis of theliterature on systemic financial risk a surveyrdquo Journal ofFinancial Stability vol 28 pp 91ndash114 2016

[10] L Corrado and T Schuler ldquoInterbank market failure andmacro-prudential policiesrdquo Journal of Financial Stabilityvol 33 pp 133ndash149 2017

[11] F Allen and D Gale ldquoFinancial contagionrdquo Journal of Po-litical Economy vol 108 no 1 pp 1ndash33 2000

[12] A Cassar and N Duffy ldquoContagion of financial crises un-derLocal and global networksrdquo Agent-Based Methods in Eco-nomics and Finance pp 111ndash131 Springer Boston MA USA2002

[13] J Duffy A Karadimitropoulou and M Parravano ldquoFinancialcontagion in the laboratory does network structure matterrdquoJournal of Money Credit and Banking vol 51 no 5pp 1097ndash1136 2019

[14] A Aleksiejuk and J A Hołyst ldquoA simple model of bankbankruptciesrdquo Physica A Statistical Mechanics and Its Ap-plications vol 299 no 1-2 pp 198ndash204 2001

[15] G Iori S Jafarey and F G Padilla ldquoSystemic risk on theinterbank marketrdquo Journal of Economic Behavior amp Orga-nization vol 61 no 4 pp 525ndash542 2006

[16] E Nier J Yang T Yorulmazer and A Alentorn ldquoNetworkmodels and financial stabilityrdquo Journal of Economic Dynamicsand Control vol 31 no 6 pp 2033ndash2060 2007


[17] F Linardi C Diks M van der Leij and I Lazier ldquoDynamicinterbank network analysis using latent space modelsrdquoJournal of Economic Dynamics And Control vol 112p 103792 2020

[18] P Gai and S Kapadia ldquoContagion in financial networksrdquoProceedings of the Royal Society A Mathematical Physical andEngineering Sciences vol 466 no 2120 pp 2401ndash2423 2010

[19] S Lenzu and G Tedeschi ldquoSystemic risk on different inter-bank network topologiesrdquo Physica A Statistical Mechanicsand Its Applications vol 391 no 18 pp 4331ndash4341 2012

[20] F Caccioli T A Catanach and J D Farmer ldquoHeterogeneitycorrelations and financial contagionrdquo Advances in ComplexSystems vol 15 Article ID 1250058 2012

[21] M Zhang J He and S Li ldquoInterbank lending networkstructure and default risk contagionrdquo Physica A StatisticalMechanics and Its Applications vol 493 pp 203ndash209 2018

[22] C P Georg and J Poschmann ldquoSystemic risk in a networkmodel of interbank markets with central bank activityrdquo JenaEconomic Research Papers Article ID S23888258 vol 332010

[23] C-P Georg ldquo+e effect of the interbank network structure oncontagion and common shocksrdquo Journal of Banking amp Fi-nance vol 37 no 7 pp 2216ndash2228 2013

[24] M L Bech J Arnold R J Glass and W E Beyeler ldquo+etopology of interbank payment flowsrdquo Physica A StatisticalMechanics and Its Applications vol 379 no 1 pp 317ndash3332007

[25] C Becher S Millard and K Soramaki)e Network Topologyof CHAPS Sterling Bank of England London UK 2008

[26] W Souma Y Fujiwara and H Aoyama ldquoComplex networksand economicsrdquo Physica A Statistical Mechanics and ItsApplications vol 324 no 1-2 pp 396ndash401 2003

[27] E B Santos and R Cont )e Brazilian Interbank NetworkStructure and Systemic Risk vol 219 2010

[28] G Iori G De Masi O V Precup G Gabbi and G CaldarellildquoA network analysis of the Italian overnight money marketrdquoJournal of Economic Dynamics and Control vol 32 no 1pp 259ndash278 2008

[29] T P Sumer and S Ozyıldırım ldquoDo banking groups shape thenetwork structure Evidence from Turkish interbank marketrdquoInternational Review of Financial Analysis vol 66 p 1013872019

[30] P McCulley ldquoTeton reflectionsrdquo PIMCO Global Central BankFocus vol 2 2007

[31] P Tucker ldquoShadow banking financing markets and financialstabilityrdquo in Proceedings of the Remarks at a Bernie GeraldCantor Partners Seminar vol 21 London UK January 2010

[32] Financial Stability Board Global Shadow Banking MonitoringReport 2015 Financial Stability Board Basel Switzerland2015

[33] T Adrian and A B Ashcraft Shadow Banking A Review of theLiterature pp 282ndash315 Palgrave Macmillan London UK2016

[34] Z Pozsar T Adrian A Ashcraft et al Shadow Bankingvol 458 no 458 pp 3ndash9 Routledge London UK 2010

[35] B S Bernanke C C Bertaut L Demarco et al ldquoInternationalcapital flows and the returns to safe assets in the United States2003ndash2007rdquo FRB International Finance Discussion Papervol 1014 2011

[36] T Wiggers and A B Ashcraft ldquoDefaults and losses oncommercial real estate bonds during the Great Depressionerardquo FRB of New York Staff Report vol 544 2012

[37] S A Ross ldquo+e economic theory of agency the principalrsquosproblemrdquo )e American Economic Review vol 63 no 2pp 134ndash139 1973

[38] F Allen and D Gale Financial Innovation and Risk SharingMIT Press Cambridge MA USA 1994

[39] E Colombo L Onnis and P Tirelli ldquoShadow economies attimes of banking crises empirics and theoryrdquo Journal ofBanking amp Finance vol 62 pp 180ndash190 2016

[40] N Gennaioli A Shleifer and R W Vishny ldquoA model ofshadow bankingrdquo )e Journal of Finance vol 68 no 4pp 1331ndash1363 2013

[41] A Moreira and A Savov ldquo+e macroeconomics of shadowbankingrdquo)e Journal of Finance vol 72 no 6 pp 2381ndash24322017

[42] C Elgin and O Oztunali ldquoShadow economies around theworld model based estimatesrdquo Bogazici University Depart-ment of Economics working Papers vol 5 pp 1ndash48 2012

[43] R M Irani R Iyer R R Meisenzahl et al)e Rise of ShadowBanking Evidence From Capital Regulation Centre forEconomic Policy Research London UK 2020

[44] N V Loayza and J Rigolini ldquoInformal employment safetynet or growth enginerdquo World Development vol 39 no 9pp 1503ndash1515 2011

[45] E Bengtsson ldquoShadow banking and financial stability Eu-ropean money market funds in the global financial crisisrdquoJournal of International Money and Finance vol 32pp 579ndash594 2013

[46] H Pan and H Fan ldquoResearch on the stability of the bankingsystem with shadow banking under macroeconomic fluctu-ationrdquo Frontiers in Physics vol 8 no 338 2020

[47] T V Dang G Gorton and B Holmstrom Opacity and theOptimality of Debt for Liquidity Provision Manuscript YaleUniversity New Haven CT USA 2009

[48] D J Watts and S H Strogatz ldquoCollective dynamics of small-networksrdquo Nature vol 393 no 6684 pp 440ndash442 1998

[49] A Barabsi and R Albert ldquoEmerge of scaling in randomnetworksrdquo Science vol 286 Article ID 509512 1999

[50] L Eisenberg and T H Noe ldquoSystemic risk in financial sys-temsrdquoManagement Science vol 47 no 2 pp 236ndash249 2001

[51] F Caccioli M Shrestha C Moore and J D Farmer ldquoStabilityanalysis of financial contagion due to overlapping portfoliosrdquoJournal of Banking amp Finance vol 46 pp 233ndash245 2014


vulnerable to financial contagions than the incompletenetwork structure under a high liquidation cost Aleksiejuket al [14] proposed a two-dimensional directed interbanknetwork model and found that there is a critical thresholdfor the average concentration of interbank deposits and theprobability of bank failure at the threshold obeys a power-law distribution Iori and Jafarey [15] built an interbanknetwork model based on random networks and stressed thatthe homogeneous interbank market makes the bankingsystem more stable while heterogeneous banks may cause achain reaction of contagion between banks Nier et al [16]also constructed a simple hierarchical network model basedon random networks and observed that a more centralizedbanking system is often more fragile Linardi et al [17]analyzed the interbank network using a dynamic latent spaceapproach and captured the core-periphery structure of fi-nancial networks By investigating the impact of the bankingnetwork structure market liquidity and idiosyncraticshocks on the stability of the banking system Gai andKapadia [18] pointed out the banking system exhibited arobust-yet-fragile tendency Moreover Lenzu and Tedeschi[19] established an agent-based interbank network modelwhich compared the stability of the banking system underthe structure of the random network and the scale-freenetwork +e results showed that in the case of heteroge-neity the random network structure is more stable than thescale-free network structure Caccioli et al [20] analyzed theeffect of different interbank network structures on the sta-bility of the banking system and found that the scale-freenetwork has better flexibility but its stability with regard tothe banking system is also significantly lower than othernetworks Zhang et al [21] studied the default risk contagionin banking systems under two different network structuresand pointed out the default risk contagion is much severerunder the random network than the endogenous networkGeorg et al [22 23] proposed an interbank network systemthat introduced the central bank as the lender of last resortand demonstrated that the money-center network is moreresilient than the random network Meanwhile there is agrowing body of research on the empirical analysis of thenetwork structure of the interbank network Soramaki et al[24] studied the interbank debt connection in Fedwire andfound that the interbank network in the United States hasthe characteristics of a small-world network When ana-lyzing the CHAPS of British Becher et al [25] pointed outthat the path length of the British interbank network is closeto that of the United States and the British interbanknetwork is also a small-world network Souma et al [26]discovered that the interbank network in Japan has scale-freestructure characteristics Edson and Cont [27] observed thatthe nodes of the Brazilian interbank network obey a power-law distribution and belong to a scale-free network Iori et al[28] found through researching the Italian real interbanklending data that the Italian interbank market networkpresents a random network structure Sumer and Ozyıldırım[29] used exposure data on the Turkish banking system tostudy the interbank network structure and showed that thecore-peripheral structure centered on highly liquid largebanks is the main interbank network structure

Indeed as the existing literature has highlighted theinterbank market is an important factor affecting the sta-bility of the banking system However from the bubble andcollapse of the financial market the shadow banking hasundergone a major dysfunction before and after the crisis+is change made shadow banking to be regarded as aninternational systemic risk transmitter and the importantfactor that undermines financial stability in times of crisis+e term shadow banking was coined byMcCulley [30] andwas picked up by policymakers [31] According to theFinancial Stability Board (FSB) [32] shadow banking is thecredit intermediation that channels funding from deposi-tors to investors through a range of securitization andsecured funding techniques and may cause systemic fi-nancial risks and regulatory arbitrage risks Althoughshadow banks conduct credit and maturity transformationsimilar to that of traditional banks shadow banks are es-sentially fragile Adrian and Ashcraft [33] pointed out thatunlike traditional banks under the policy safety net thefunds of depositors in shadow banks are not protectedPozsar et al [34] compared the size of shadow bankingduring the crisis and found that before the crisis the size ofshadow banking showed a sudden growth trend andreached a peak Bernanke et al [35] discussed that shadowbanks use maturity transformation to avoid risks butfragile assets and liabilities caused shadow banks to collapseexcessively during the crisis and systemic risks increaseddramatically By documenting the performance of shadowbanking Wiggers and Ashcraft [36] observed that shadowbanks defaulted in large numbers in times of crisis whichdestroyed the banking system stability Nevertheless Ross[37] Allen and Gale [38] stressed that the financing ex-pansion of shadow banking is in line with Paretorsquos optimalimprovement which can share part of the systemic risk andmaintain the stability of the banking system Colombo et al[39] constructed a shadow banking model and emphasizedthat the form of propagation after the crisis shock wouldreduce the system to resist risks and the correspondingstability level of the banking system An improved shadowbanking model is proposed by Gennaioli et al [40] and theresults showed that investors ignore tail risk which couldmake the banking system vulnerable to crisis shocks butunder rational expectation shadow banking would help toresist systemic risk and maintain system stability Moreiraand Savov [41] built a macro-finance model of shadowbanking and argued that shadow banking expands the li-quidity provision as well as builds up the fragility of thesystem Elgin and Oztunali [42] noted through a two-sectordynamic general equilibrium model that the relative size ofshadow banking will influence the banking systemrsquos sta-bility Besides Irani et al [43] investigated the connectionsbetween bank capital regulation and the lightly regulatedshadow banks Loayza et al [44] and Elias [45] qualitativelyanalyzed the effect of shadow banking on the bankingsystemrsquos stability from the perspective of the labor marketand the money market fund respectively

Previous research on the impact of shadow banking onthe banking systemrsquos stability has been carried out from theaspects of qualitative analysis related to changes in shadow




2 The Model











minus 1113944τ

k1Ii(t minus k)

(1)










+ ρ 1113944τ


(2)


τk1 Ii(t minus


ρ 0 1 minus q

ρ q1113896 (3)





(4)

Shadowbank 1

Traditionalbank 1

Traditionalbank 2

Traditionalbank U

Shadowbank 2

Shadowbank 3

Shadowbank V

Balance sheet

LiquidityLi (t)


Bi (t)


InvestmentIi (t)

Central bank

(b)

(c)

(a)














Cij(t)

Ei(t)lowastbij(t)

1113936fj1 bij(t)


0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)


fj1 bij(t) is














R(t) 1

WOe

1113944

Oe

i11113944

t+W

jt+1

Yij

Yij + Z

ij

(8)


j andZi



PC n1

n (9)



DC 1113936

n1i1 n

i2G1113872 1113873

n1 (10)


4 Results










started 50


f


shadow bank3






0 20 40 60 80Timestep

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

Random


InvestmentDividend

(a)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

0 20 40 60 80Timestep

Small-world


InvestmentDividend

(b)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney


InvestmentDividend

0 20 40 60 80Timestep

Scale-free

(c)


0 20 40 60 80Timestep

02

04

06

08

1

Surv

ival

ratio


(a)


0 20 40 60 80Timestep

0

02

04

06

08Sy

stem

ic ri

sk

(b)





0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)











0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References
























































2 The Model











minus 1113944τ

k1Ii(t minus k)

(1)










+ ρ 1113944τ


(2)


τk1 Ii(t minus


ρ 0 1 minus q

ρ q1113896 (3)





(4)

Shadowbank 1

Traditionalbank 1

Traditionalbank 2

Traditionalbank U

Shadowbank 2

Shadowbank 3

Shadowbank V

Balance sheet

LiquidityLi (t)


Bi (t)


InvestmentIi (t)

Central bank

(b)

(c)

(a)














Cij(t)

Ei(t)lowastbij(t)

1113936fj1 bij(t)


0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)


fj1 bij(t) is














R(t) 1

WOe

1113944

Oe

i11113944

t+W

jt+1

Yij

Yij + Z

ij

(8)


j andZi



PC n1

n (9)



DC 1113936

n1i1 n

i2G1113872 1113873

n1 (10)


4 Results










started 50


f


shadow bank3






0 20 40 60 80Timestep

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

Random


InvestmentDividend

(a)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

0 20 40 60 80Timestep

Small-world


InvestmentDividend

(b)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney


InvestmentDividend

0 20 40 60 80Timestep

Scale-free

(c)


0 20 40 60 80Timestep

02

04

06

08

1

Surv

ival

ratio


(a)


0 20 40 60 80Timestep

0

02

04

06

08Sy

stem

ic ri

sk

(b)





0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)











0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References
























































minus 1113944τ

k1Ii(t minus k)

(1)










+ ρ 1113944τ


(2)


τk1 Ii(t minus


ρ 0 1 minus q

ρ q1113896 (3)





(4)

Shadowbank 1

Traditionalbank 1

Traditionalbank 2

Traditionalbank U

Shadowbank 2

Shadowbank 3

Shadowbank V

Balance sheet

LiquidityLi (t)


Bi (t)


InvestmentIi (t)

Central bank

(b)

(c)

(a)














Cij(t)

Ei(t)lowastbij(t)

1113936fj1 bij(t)


0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)


fj1 bij(t) is














R(t) 1

WOe

1113944

Oe

i11113944

t+W

jt+1

Yij

Yij + Z

ij

(8)


j andZi



PC n1

n (9)



DC 1113936

n1i1 n

i2G1113872 1113873

n1 (10)


4 Results










started 50


f


shadow bank3






0 20 40 60 80Timestep

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

Random


InvestmentDividend

(a)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

0 20 40 60 80Timestep

Small-world


InvestmentDividend

(b)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney


InvestmentDividend

0 20 40 60 80Timestep

Scale-free

(c)


0 20 40 60 80Timestep

02

04

06

08

1

Surv

ival

ratio


(a)


0 20 40 60 80Timestep

0

02

04

06

08Sy

stem

ic ri

sk

(b)





0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)











0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References
































































Cij(t)

Ei(t)lowastbij(t)

1113936fj1 bij(t)


0 otherwise

⎧⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎩

(7)


fj1 bij(t) is














R(t) 1

WOe

1113944

Oe

i11113944

t+W

jt+1

Yij

Yij + Z

ij

(8)


j andZi



PC n1

n (9)



DC 1113936

n1i1 n

i2G1113872 1113873

n1 (10)


4 Results










started 50


f


shadow bank3






0 20 40 60 80Timestep

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

Random


InvestmentDividend

(a)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

0 20 40 60 80Timestep

Small-world


InvestmentDividend

(b)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney


InvestmentDividend

0 20 40 60 80Timestep

Scale-free

(c)


0 20 40 60 80Timestep

02

04

06

08

1

Surv

ival

ratio


(a)


0 20 40 60 80Timestep

0

02

04

06

08Sy

stem

ic ri

sk

(b)





0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)











0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References

























































R(t) 1

WOe

1113944

Oe

i11113944

t+W

jt+1

Yij

Yij + Z

ij

(8)


j andZi



PC n1

n (9)



DC 1113936

n1i1 n

i2G1113872 1113873

n1 (10)


4 Results










started 50


f


shadow bank3






0 20 40 60 80Timestep

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

Random


InvestmentDividend

(a)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

0 20 40 60 80Timestep

Small-world


InvestmentDividend

(b)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney


InvestmentDividend

0 20 40 60 80Timestep

Scale-free

(c)


0 20 40 60 80Timestep

02

04

06

08

1

Surv

ival

ratio


(a)


0 20 40 60 80Timestep

0

02

04

06

08Sy

stem

ic ri

sk

(b)





0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)











0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References

























































0 20 40 60 80Timestep

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

Random


InvestmentDividend

(a)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney

0 20 40 60 80Timestep

Small-world


InvestmentDividend

(b)

ndash100

0

100

200

300

400

500

Am

ount

of m

oney


InvestmentDividend

0 20 40 60 80Timestep

Scale-free

(c)


0 20 40 60 80Timestep

02

04

06

08

1

Surv

ival

ratio


(a)


0 20 40 60 80Timestep

0

02

04

06

08Sy

stem

ic ri

sk

(b)





0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)











0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References
























































0 20 40 60 80Timestep (ρ = 0025)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0045)

(b)

0

02

04

06

08

Syste

mic

risk


0 20 40 60 80Timestep (ρ = 0065)

(c)


0015 0025 0035 0045 0055 00650

02

04

06

08

1

PC

ρ

(d)


0015 0025 0035 0045 0055 00650

01

02

03

04

05

06

DC

ρ

(e)











0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References






























































0 20 40 60 80Timestep (τ = 2)

0

0005

001

0015

002Sy

stem

ic ri

sk


(a)

Timestep (τ = 4)

Syste

mic

risk

0 20 40 60 800

02

04

06

08

1


(b)

Timestep (τ = 6)

Syste

mic

risk

0

02

04

06

08

1

0 20 40 60 80


(c)

2 3 4 5 60

02

04

06

08

1

PC

τ


(d)

2 3 4 5 60

02

04

06

08

DC

τ


(e)







0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References


























































0 20 40 60 80Timestep (Andash = 750)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (Andash = 950)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (Andash = 1150)

0

02

04

06

08

Syste

mic

risk


(c)

750 850 950 1050 1150Andash

0

02

04

06

08

1

PC


(d)

750 850 950 1050 1150Andash

0

02

04

06

08

DC


(e)



0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References






















































0 20 40 60 80Timestep (ra = 0003)

0

02

04

06

08

1Sy

stem

ic ri

sk


(a)

0 20 40 60 80Timestep (ra = 0004)

0

02

04

06

08

1

Syste

mic

risk


(b)

0 20 40 60 80Timestep (ra = 0005)

0

02

04

06

08

1

Syste

mic

risk


(c)

0001 0002 0003 0004 0005ra

0

02

04

06

08

1

PC


(d)

0001 0002 0003 0004 0005ra

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (d = 02)

0

0005

001

0015

002

0025

Syste

mic

risk


(a)

0 20 40 60 80Timestep (d = 05)

0

01

02

03

04

Syste

mic

risk


(b)

0 20 40 60 80Timestep (d = 08)

0

02

04

06

08

1

Syste

mic

risk


(c)

Figure 8 Continued



5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References























































5 Conclusions





02 04 06 08d

0

02

04

06

08

1

PC


(d)

02 04 06 08d

0

01

02

03

04

05

06

DC


(e)


0 20 40 60 80Timestep (loss = 015)

0

02

04

06

08

1

Syste

mic

risk


(a)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 030)

(b)

0

02

04

06

08

1

Syste

mic

risk


0 20 40 60 80Timestep (loss = 045)

(c)










Data Availability




Acknowledgments


References





























































Data Availability




Acknowledgments


References






















































thestabilityofbankingsystemwithshadowbankingondifferent interbank … · 2020. 12. 21. ·...

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