复杂网络科学导论 (1).pdf

This article was downloaded by:University of Saskatchewan LibraryOn:02 September 2012,At:03:04Publisher:RoutledgeInforma Ltd Registered in England and Wales Registered Number:1072954 Registered office:MortimerHouse,37-41 Mortimer Street,London W1T 3JH,UKQuantitative FinancePublication details,including instructions for authors and subscription information:http:/ topology of the interbank marketMichael Boss a,Helmut Elsinger b,Martin Summer a&Stefan Thurner ca Oesterreichische Nationalbank,Otto-Wagner-Platz 3,A-1011 Wien,Austriab Department of Finance,Universitt Wien,Brnner Strasse 71,A-1210 Wien,Austriac Complex Systems Research Group,HNO,Medical University Vienna,Whringer Grtel1820,A-1090 Wien,Austria E-mail:Version of record first published:18 Aug 2006To cite this article:Michael Boss,Helmut Elsinger,Martin Summer&Stefan Thurner(2004):Network topology of theinterbank market,Quantitative Finance,4:6,677-684To link to this article:http:/dx.doi.org/10.1080/14697680400020325PLEASE SCROLL DOWN FOR ARTICLEFull terms and conditions of use:http:/ article may be used for research,teaching,and private study purposes.Any substantial or systematicreproduction,redistribution,reselling,loan,sub-licensing,systematic supply,or distribution in any form toanyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date.The accuracy of any instructions,formulae,and drug dosesshould be independently verified with primary sources.The publisher shall not be liable for any loss,actions,claims,proceedings,demand,or costs or damages whatsoever or howsoever caused arising directly orindirectly in connection with or arising out of the use of this material.QUANTITATIVEFINANCEVOLUME4(DECEMBER2004)677684RE S E A R C HPA P E RTAYLOR&FRANCISLTDtandf.co.ukNetwork topology of the interbank marketMichael Boss1,Helmut Elsinger2,Martin Summer1and Stefan Thurner3,41Oesterreichische Nationalbank,Otto-Wagner-Platz 3,A-1011 Wien,Austria2Department of Finance,Universita t Wien,Bru nner Strasse 71,A-1210 Wien,Austria3Complex Systems Research Group,HNO,Medical UniversityVienna,Wa hringer Gu rtel 1820,A-1090 Wien,AustriaE-mail:thurnerunivie.ac.atReceived 19 February 2004,in final form 6 August 2004Published 18 April 2005Online at www.tandf.co.uk/journals/titles/14697688.asp DOI:10.1080/14697680400020325AbstractWe provide an empirical analysis of the network structure of theAustrian interbank market based on Austrian Central Bank(OeNB)data.The interbank market is interpreted as a network where banks arenodes and the claims and liabilities between banks define the links.Thisallows us to apply methods from general network theory.We find thatthe degree distributions of the interbank network follow power laws.Given this result we discuss how the network structure affects thestability of the banking system with respect to the elimination of a nodein the network,i.e.the default of a single bank.Further,the interbankliability network shows a community structure that exactly mirrors theregional and sectoral organization of the current Austrian bankingsystem.The banking network has the typical structural features found innumerous other complex real-world networks:a low clusteringcoefficient and a short average path length.These empirical findings arein marked contrast to the network structures that have been assumedthus far in the theoretical economic and econo-physics literature.1.IntroductionThe problem of systemic riskthe large-scale breakdownof financial intermediationhas been a key concern forinstitutions in charge of safeguarding financial stability,mainly central banks and regulators.Systemic risk is animportant issue in the banking system because banks areusually linked by a complex network of mutual creditrelations originating from their activities in the interbankmarket.Through this network of interbank liabilitieswhich connects individual institutions the failure of onebank might directly cause the failure of another bank ina domino effect.From an abstract viewpoint the system ofmutual credit relations among financial institutions can beviewed as a network,where banks are the nodes and theirinterbank relations form financial links.An importantproblem is to understand how the structure of thisinterbank network affects the financial stability propertiesof the banking system as a whole.This paper takes a firststep in this direction by uncovering the empirical structureof an interbank network using a data set provided by theAustrian Central Bank.4Author to whom any correspondence should be addressed.1469-7688 Print/1469-7696 Online/04/0606778?2004 Taylor&Francis Ltd677Downloaded by University of Saskatchewan Library at 03:04 02 September 2012 In our analysis we can draw on insights and conceptsfrom ongoing and very active interdisciplinary researchon networks.The physics community,in particular,hasgreatly contributed to the empirical analysis and to afunctional understanding of the structure of complexreal-world networks in general;see 1,2 for an overview.Perhaps one of the most important contributions torecent network theory is an interpretation of networkparameters with respect to the stability,robustness,andefficiency of the underlying system;see e:g:3,4.Clearly,these insights are relevant for the issues of financialstability and the network structure of the mutual creditrelations in the interbank market.Our main finding is that the network structure of theinterbank market is scale free,i:e:it shows power lawsin the degree distributions.This means that there are veryfew banks with many interbank linkages,whereas thereare many with only a few links.This feature of networkshas repeatedly been related to the stability of networkswith respect to the random breakdown of nodes,and,atthe same time,to the risk of the specific removal of hubs,i:e:the very few well connected nodes in the network.Inthe present context,this means thatgiven the actuallyobserved structure of interbank claims and liabilitiesthebanking system is relatively robust with respect todomino effects caused by the random breakdown ofsingle institutes.However,the existence of power laws inthe system implies the existence of hubs,the specificremoval of which can have a dramatic impact on thestability of the system,and could ultimately lead to thecollapse of the entire financial system.We also describeother specific features of the network such as lowclustering and short average distances between institu-tions,which confirm the general structural characteristicsof the interbank network that we find in the data.Finally,another message of this work is that it providesa direct insight into the structure of a real interbanknetwork and its contract size distributions,which couldbe helpful for imposing restrictions on the large classesof potential networks for future modeling of interbankrelations.While our paper is the first to provide an empiricalanalysisofthestructuralfeaturesofareal-worldinterbank network using concepts from modern networktheory,the topic of systemic risk and domino effects hasbeen studied previously by various authors.In theeconomic literature the notion of systemic risk has beenapplied more broadly to refer to a fairly large variety ofphenomena.It is used to describe various types of crisesranging from payment systems,bank runs,and spillovereffects between financial markets,to a very broadlyunderstood notion of financially driven macroeconomiccrises;see 57 for a more detailed overview.In thecontext of banking,the problem is often considered that,due to the tight inter-dependencies between the differentbanks in a banking system,problems can suddenlyoccur at many banks simultaneously and might disruptfinancial intermediation on a large scale.Clearly,froma network perspective this domino effect aspect ofinsolvency is the part of the systemic risk literature ourpaper relates to.One might classify the contributions of the presentliterature into two broad categories:theoretical networkstudies,on the one hand,and empirical papers,mostlycombined with simulations,on the other.From atheoretical point of view,the economics literature oncontagion 810 suggests various network topologies thatmight be interesting to look at.Allen and Gale 8 suggestthe study of a fully connected graph of mutual liabilities.The properties of a banking system with this structure arethen compared with the properties of systems with non-fully connected networks,where an explicit example isgiven for a situation where a fully connected network ismore conducive for financial stability than an incompleteone.Freixas et al 9 contrast a circular graph with a fullyconnected graph,and Thurner et al 10 studies a muchricher set of different network structures which areused in an agent-based model where banks minimizeindividual risk.Iori et al 11 study systemic risk in asimulation model without studying the impact of thenetwork structure explicitly.There is also a large bodyof economics literature dealing with networks moregenerally.This mainly game theoretic literature is,however,mostly unconcerned with financial networksand financial stability in particular.A fairly comprehen-sive overview of this literature is given by Jackson 12.An important theoretical paper from the operationsresearch literature is that of Eisenberg and Noe 13,where the authors study a centralized static clearingmechanism for a financial system with exogenous incomepositions and a given structure of bilateral nominalliabilities.They provide a deterministic method to makethe payment promises and the exogenous income posi-tions consistent by an insolvency procedure which rationscreditors in the system,if necessary.However,to use thisanalysis in the context of risk assessment,some param-eters of the model have to be stochastic such as theexogenous income positions.One can think of them asrandom variables on a space of risk factor changes.Suchan extension is suggested by Elsinger et al 14,15.Herethe authors take data from the Austrian interbankmarket to quantitatively describe the network of bilateralliabilities and study how shocks to the exogenous incomepositions are propagated throughout the system.Foreach realization of the exogenous income position themodel of Eisenberg and Noe 13 pins down a uniqueclearing vector of payments between banks.From thisinformation,one can deduce which banks are insolvent.The distribution of insolvency cases can then be simulatedand default probabilities for individual institutions can bededuced.Moreover,one can determine which insolvencycases occur indirectly due to contagion.The impact ofnetwork structure on contagion flow through the systemby simulation has been analysed by Boss et al 16.678M Boss et alQUANTITATIVEFINANCEDownloaded by University of Saskatchewan Library at 03:04 02 September 2012 Some of the empirical,simulation-based literature onfinancial networks has taken the approach of measuring aliability network and studying the propagation of certainshocks through the network.The papers have mainlyworked with data sets from the payment system 17,18or with interbank data 1922.All of these studiesinvestigate contagious defaults that result from thehypothetical failure of a single institution.Elsingeret al 14,15 take these studies one step further bycombining the analysis of interbank connections with asimultaneous study of the banking systems overall riskexposure.Instead of performing a banking risk analysison ad hoc single institution failure scenarios,they studyrealistic risk scenarios for the banking system which aresimulated using standard risk management techniques.Our approach provides a complementary point ofview in relation to this literature.The analysis of networkstructure as suggested in this paper is able to explain someof the results derived in some of the simulation studiescited above.For instance,the authors of 14,15,1922unanimously find that contagion of insolvency occursrelatively rarely under realistic risk scenarios.The powerlaws found in the network structure of the Austrianinterbank market and its consequences provide a naturalexplanation for these results.The paper is organized as follows.Section 2 containsour conceptual description of the interbank data withtools from network theory.Section 3 contains ourempirical results.In section 4 we discuss our findingsand explore their economic and potential regulatoryconsequences.2.The banking networkThe interbank network is characterized by the liability(or exposure)matrix L.The entries Lijare the liabilitiesbank i has towards bank j.We use the convention ofwriting liabilities in the rows of L.If the matrix is readcolumn-wise(transposed matrix LT)we see the claims orinterbank assets that the banks hold with each other.Note that L is a square matrix,but not necessarilysymmetric.The diagonal of L is zero,i:e:no bank self-interaction exists.In the following we are looking for thebilateral liability matrix L of all(about N900)Austrianbanks,the Central Bank(OeNB)and an aggregatedforeign banking sector.Our data consist of ten Lmatrices,each representing liabilities for quarterly singlemonth periods between 2000 and 2003.To obtain theAustrian interbank network from Central Bank datawe draw upon two major sources:we exploit structuralfeatures of the Austrian bank balance sheet data base(MAUS)and the major loan register(GKE)in combina-tion with an estimation technique.The Austrian banking system has a sectoral organi-zation for historical reasons.Banks belong to one ofseven sectors:savings banks(S),Raiffeisen(agricultural)banks(R),Volksbanken(VB),joint stock banks(JS),state mortgage banks(SM),housing construction savingsandloanassociations(HCL),andspecialpurposebanks(SP).Banks have to break down their balancesheet reports on claims and liabilities with other banksaccording to the different banking sectors,the CentralBank and foreign banks.This practice of reporting onbalance interbank positions breaks the liability matrix Ldown into blocks of sub-matrices for the individualsectors.The savings banks and the Volksbanken sectorare organized in a two-tier structure with a sectoral headinstitution.The Raiffeisen sector is organized by a three-tier structure,with a head institution for every federalstate of Austria.The federal state head institutions havea central institution,Raiffeisenzentralbank(RZB),whichis at the top of the Raiffeisen structure.Banks with ahead institution have to disclose their positions with thehead institution,which gives additional information on L.Since many banks in the system hold interbank liabilitiesonly with their head institutions,one can pin down manyentries in the L matrix exactly.This information is thencombined with the data from the major loans register ofOeNB.This register contains all interbank loans abovea threshold of 360000 Euro.This information providesus with a set of constraints(inequalities)and zerorestrictions f