Agent-based Networks of Corporate...

Agent-based Networks of Corporate Lending

Grzegorz Ha laj

European Central Bank

26/03/2015

Parts based on research with U. Kochanska (ECB) and Ch. Kok (ECB)DISCLAIMER: This presentation should not be reported as representingthe views of the European Central Bank (ECB). The views expressed arethose of the authors and do not necessarily reflect those of the ECB

Grzegorz Ha laj (ECB) Systemic Risk and Financial Networks, IPAM 26/03/2015 1 / 30

MotivationRecent financial crisis: loss of trust on the interbank market; concernsabout failure of one of the key players spreading contagion; smallshocks with detrimental effectsA response from regulators: measures to mitigate the risk ⇒ highercapital standards + reducing bilateral exposures

I Large Exposure limits;I Credit Valuation Adjustment to unlock the risk in OTC exposures and

immediately reflect it in the capitalI Standard settlement practices (CCP framework)I ...but usually only interbank market modelled → a large part of the

network is neglectedOur aim:

I fill the gap in the literature to improve understanding of:F linkages (and emergence of links) between banks and the real economy

(non-bank corporate sector)F risk stemming from interconnectedness

Approach: modelling of banks’ reactions to these measures and to thechanging macroeconomic environment with links to corp sector(combining risk/return trade-offs, funding conditions...)


Outline

Modeling framework – agent-based interbank+corporate networks

Four round model – endogenous formation

Interbank augmented by non-bank corporate sector (called: firms)1 offers of interbank placements based on individual optimisation of

interbank asset structures2 funding diversification3 negotiation phase: matching offers and preferred funding structure in a

bargaining game4 price (i.e. interest rate) adjustment (if demand 6= supply)

Scope for application

stress tests and dynamic balance sheet tool

assessing network effects of credit provision to the real economy(shocks from corporate sector)

parametrisation of LE and concentration limits (so far only forinterbank) and sector RWs


Literature – towards network formation

Networks in other research areas: game theory of Jackson andWolinsky (1996)

Extensions in finance – exogenous networks: game theory – optimalresponses of banks to shocks to incentives to lend Cohen-Cole (2011);Bluhm et al. (2013). Acemoglu et al. (2013): dealing with socialinefficiency of financial networks; Georg (2011) models interbankexposures as residuals of banks’ investment activities (but networkssimply drawn from a distribution)

Jackson and Watts (2002) combine stochastic games and matchingproblems to study general principles of network formation ineconomics; Acemoglu et al. (2014) create the interbank structurebased on equilibrium of lending contracts and repayments

Agent-based approach to address overly complex equilibria – Markose(2012); Grasselli (2013)

Matching (Chen, 2013); (Duffie and Sun 2012) and price formation(Eisenschmidt, 2009) ⇒ mechanisms important for us


Formation of the lending network – Endogenous networks

The aim of the project is to:

1 understand foundations of the topology of lending networks in theeconomy

2 capture sensitivity of the interbank network structures to theheterogeneity of banks (in terms of size of balance sheet, capitalposition, general profitability, counterparty credit risk) and thechanges of market and bank specific risk parameters

3 provide a framework to assess effectiveness of rule designed tomitigate systemic risk on the interbank system (esp. pertaining tocapital requirements, size and diversity of interbank exposures)


4 round model – outlineThe following 4 rounds are repeated until 'all interbank assets of apredefined volume are invested (separate for interbank and bank-firmnetwork)

1 Firms make loan offers to other banks and firms which are drawnfrom a probability map: offers based on optimisation of theirinterbank asset structures and corporate lending portfolio

2 Firms formulate their preferred structure of interbank (banks) andbank (firms) funding from banks drawn in round 1: based on thediversification of the funding (rollover) risk

3 Firms enter negotiation phase: bargaining game in order to try tomatch the preferred allocation of the assets and the preferredstructure of interbank (bank) funding

4 Firms reconsider their pricing offers: firms with open funding gapincrementally adjust their offers of interest payments on new loan(optional feature, not used so far in the exposition)

At each step, assets are “matched” with liabilities incrementally


Figure 1: The sequential four round procedure of the interbank formation(formation of bank-firm links separate but analogous)

2) OPTIMISATIONPreferred asset

structure

1) OPTIMISATIONPreferred funding

structure 4) PRICEInterest rate adjustment

3) BILATERAL GAMESBargaining game

STEPS Repeateduntil all IB assetsare allocated

Unallocated IB assets and liabilities

NEW PLACEMENTSPart of unallocated IB assetsplaced in banks as deposits

creating IB linkages

4 ROUNDS

REPEATED

STEPS

Next step

Full allocation IB Network Completed

Partial allocation

INITIAL PARAMETERSAggregate IB lending / borrowing, capital, RWA, CDS

spreads, market interest rates


Prerequisites

(nodes) N banks and M non-bank firms: capital and bank borrowing+ out-degree distribution within (NACE) sectors

(exposures) Let Lij denotes the interbank (bank) placement (loan) ofbank j in bank (firm) i .

(capital position – constraint for risk-taking) total capital e andcapital e I ≤ e allocated to the interbank assets, eC ≤ e allocated tonon-bank firms; risk weights ω of exposures.

(probability map P) of interbank and bank-firm connections drawnfrom P allowing for capturing possible customer relationship betweenbanks and firms. Each bank j draws its counterparties Bk

j ⊂ N/{j},enlarging the set at each step k : Bk+1

j = Bkj ∪ Bk+1

j ;In addition, firms choose max number (mj) of banks granting loansbased on out-degree distribution, i.e. #Bk+1

j ≤ mj

(matching) at step k incremental matching of assets and liabilities:akj = ak−1

j −∑

i Lkij , where Lk is a matrix of placements at step k


1st round – Criteria for investment of interbank assets

General idea of banks’ optimising behaviour

Assumption (i): each bank maximises return from loan portfolio adjustedby risk related to interest rates and counterparts’ defaults (with apredefined risk aversion parameter) and taking into account customerrelationship, i.e. a drawn sample of banks and firmsAssumption (ii): optimisation of interbank portfolio separate fromoptimisation of non-bank corporate loan portfolio

Each bank maximises the following function of its interbank exposurebreakdown:

J(L1j , . . . , LNj) =∑i∈Bk

j

riLij − κj(σ ∗ L>·j )>Q(σ ∗ L·j) (1)

Outcome: a matrix of exposures LI ,k , whereby optimisation subject toconstraints...


...Constraints of the admissible set of strategies

The maximisation is subject to some feasibility and capital constraints.

1 budget constraint:∑

j |j 6=i Lij = akj and Ljj = 0, for a0j = aj being

exogenously determined;

2 counterpart’s size constraint: Lij ≤ lki ;

3 capital constraint:∑

i |i 6=j ωi (Lkij + Lij) ≤ e Ij − γ>(L·j + L·j);

4 large exposure limit constraint: Lij ≤ χej .What if the constraints are too stringent for a bank j? ⇒ bank j reducesits interbank lending and (technically) the optimisation is solved for akjreplaced by aki − 2∆aki , aki − 3∆aki ,... until aki − ki∆aki gives a feasible setof constraints


2nd round – funding diversification

Diversification risk gauged by default risk

Xj : =

{0 with probability pj1 with probability 1− pj

(2)

Assumption: pjs are risky (variance based on time series of CDS spreads)For a covariance matrix D2

X of X , the optimised funding risk is measured

F (Lki1, . . . , LkiN) = κF [Lki1 . . . LkiN ]D2

X [Lki1 . . . LkiN ]> (3)

Outcome: a matrix of interbank deposits LF ,k , whereby optimisation onthe admissible set:AF

i : = {y ∈ RN+|j ∈ Bk

j ⇒ yj ≤ akj and j 6∈ Bkj ⇒ yj = 0}.

REMARK: inclusion of non-bank corporate sector implies that (3) is alsosolved by non-bank firms (⇒ LF ,k is (N + M)× (N + M) matrix)


3rd round – the game

Assumption: banks negotiate loans in pairs simultaneously (pair (i ′, j)knows the outcome of (i ′′, j) after both games are completed). Case

LI ,kij > LF ,kij

G kij (x) =

[U l ,k∗ij − s l ,kij · (x − LF ,kij )

] [Ua,k∗ij − sa,kij · (L

I ,kij − x)

](4)

where s l ,kij is a measure of how much bank i is willing to deviate from hisoptimal funding strategy, i.e.

s l ,kij = max

(U l ,kij (LF ,kij )− U l ,k

ij (LI ,kij )

|LI ,kij − LF ,kij |, 0

),

where U l ,kij (x) = −F (LF ,ki1 , . . . , LF ,kij−1, x , L

F ,kij+1, . . . , L

F ,kiN )

(for sa,kij analogously,... and for LI ,kij < LF ,kij similar)

Goal of the game: maximisation of G kij ; outcome → LG ,I ,k and LG ,F ,k


3rd round – correction to the game

Observation: the outcome of the game may not be consistent with thebudget constraint of the given size of banks’ aggregate interbank portfolios(i.e. ak and lk)

Correction

if∑

i LG ,I ,kij > akj then LG ,I ,kij := LG ,I ,kij ∗ akj∑

i LG ,I ,kij

if∑

j LG ,F ,kij > lki then LG ,F ,kij := LG ,F ,kij ∗ lki∑

j LG ,F ,kij

LG ,k = min(LG ,I ,k , LG ,F ,k) (element-wise)

Aggregation of the step k with outcomes of steps 1, . . . , k − 1

Lk+1 = Lk + LG ,k

Update: e I ,k+1, ak+1 and lk+1


4th round – price adjustment [optional]

After the first 3 rounds of a step k some banks may still have a gap inthe interbank funding ⇒ adjustment to the offered interest rate onnew interbank deposits to increase a chance to obtain funding in stepk + 1

If at the step k + 1 the gap amounts to gk+1i : = li −

∑j L

k+1ij then

the adjusted offered rate satisfies rk+1i = rki exp(αgk+1

i /li ).

REMARKS

in the baseline case we assume α = 0.25

no clearing mechanism implemented – would be good to have it sinceprice adjustment mechanism does not prove to be fully effective (asequential 4-round model with only one step and price adjustmentdoes not lead to full allocation of assets / liabilities)


Sensitivity analysis based on a stylised setup

Assumptions

100 banks (bank ∈ {1, . . . , 100})uniform probability map (5% probability of connection for all pairs ofnodes)

uniform return (0.05) and investment risk (0.1) and funding risk (0.1)parameters

no correlation


Scenario 1: Risk of investment on the interbank becomeheterogenous (part 1)

x-axis: banks

y-axis: betweennesscentrality

light copper linescorrespond to the baselinecase; the darker the colorthe higher heterogeneity ofinvestment risk (σline

bank =

σbasebank + line ∗ dσ ∗ bank

100)

Centrality of more ‘risky’nodes decreases and the(relatively) less ‘risky’increases

Figure 2: Betweenness centrality vs changing riskof the return from interbank investment

0 20 40 60 80 100

0.0080

0.0085

0.0090

Source: own calculations



x-axis: banks

y-axis: Marginal (of laststep tranche) price


bank =


100)

(Unsurprisingly) price paidby banks that have moreinvestment risk increasessince they must searchlonger for funding.

Figure 3: Marginal price vs changing risk of returnfrom interbank investment

0 20 40 60 80 1000.021

0.022

0.023

0.024

0.025

0.026

0.027




x-axis: banks

y-axis: clusteringcoefficient


bank =


100)

Heterogeneity of risktranslates into uniformshift of number of trianglesassociated with nodes.

Figure 4: Clustering coeff. vs changing risk ofinvestment into interbank assets

0 20 40 60 80 1000.170

0.175

0.180

0.185

0.190

0.195



Scenario 2: Risk of investment on the interbank becomeheterogenous

x-axis: banks

y-axis: Betweennesscentrality

light copper linescorrespond to the baselinecase; the darker the colorthe higher heterogeneity offunding risk (σline

bank =


100)

Centrality of more ‘risky’nodes decreases and the(relatively) less ‘risky’increases

Figure 5: Betweenness centrality vs changing riskof the funding (roll-over) risk

0 20 40 60 80 100

0.0080

0.0085

0.0090



Table 1: Overview of data inputs

Item Description Sources

CoverageBanks As identified in 2011 EBA Disclosures; 80 banks from EU countries.

+ 500 randomly generated banks based on TAEBA, Halaj and Kok (2014)+ Bankscope

Non-financial corpo-rations

Members of the benchmark equity indices in the countries coveredby EBA Disclosures and Halaj and Kok (2014); total 700 firms

Bloomberg and ECB

AttributesBanks Total assets, IB assets, securities, securities MtM, equity, CT1 cap-

ital, IB liabilitiesEBA

Banks Loans to non-fin. corporations: calculated by using avg. countryratio of such loans to TA based on the ECB (MFI) balance sheetdataset

ECB calculations

Banks Economic activity code (NACE), CDS of senior debt with 5 maturity,and long-term issuer ratings by Moody’s, Fitch and S&P.

Bloomberg


Total assets, total equity, total liabilities, NACE code, CDS spreadsof senior debt with 5 maturity, and long term ratings by Moody’s,Fitch and S&P.

Bloomberg


Loans from banks: calculated by using the average country ratioof loans to total assets of NFCs based on the ECB EA Accountsdataset.

ECB calculations

Lending relations and other supportive variablesLending relationship Defined as the number of loans with different banks; average figures

by country and NACE sector were applied based on the data providedthrough the Working Group on Credit Registers

ECB calculations

Interest rates onloans by size andcountry

Avg. interest rates on loans by size of loan and by country basedon the ESCB MIR data; categories of loans as follows: (below 0.25EUR mn), (equal or above 0.25-1 EUR mn), and (over 1 EUR mn).

ECB calculations

Expected default fre-quencies

Avg. of expected default frequencies for non-financial corp. bycountry and NACE.

Moody’s KMV and ECB


Sampling of the network

Observed nodes (banks + non-bank corporate firms) and +500generated banks

I generated banks: based on the total assets and proportional allocationof other attributes

Lending relationship:I {bank}–{firm}: based on aggregate Credit Register data

F → out-degree distribution (for each NACE sector) → the cardinalnumber of set Bk

j of firms k to which a bank j grants loans isconstrained by a number mj drawn from the out-degree distribution,i.e. #Bk

j ≤ mj

+F → probability that a bank in a given country lends to a firm from a

given country and a given (NACE) sector

I {EBA sample bank}–{EBA sample bank}: EBA disclosuresI {small bank}–{EBA sample bank}: arbitrary [small] probability of

connection (= 0.01)


Figure 6: Network of non-bank corporate borrowing

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Applications – policy implications

Event-driven contagion (realised)

Deterioration of credit quality in a given sector (NACE) – corporate loan lossestrigger contagion

Risk weights – policy tool to limit exposures to risky sectors (realised)

Specific sectors can be targeted to force banks to use more capital for more riskysectors

Large Exposure limits – compactness of the networks (realised)

lower bilateral exposures allowed ⇒ more connections

Network reactions to adverse market conditions (planned)

passing macro scenarios via dynamic BS model (Ha laj, 2013):baseline macro scenario ⇒ optimising behaviour of banks ⇒ change in banks’ preferred

aggregate interbank lending and borrowing ⇒ endogenous formation of the interbank under

specified regulatory regime ⇒ adverse macro shock ⇒ banks defaults ⇒ contagion


Figure 7: Contagion simulation

BE HU LU PT

AT CY DE DK ES FI FR GB GR IE IT NL NO SE SI

Consumer, Non-cyclical [7]Consumer, Cyclical [8]Non-bank financial [11]

Consumer, Non-cyclical [1]Energy, Basic materials [2]

Contagion mechanism – cascade triggered by a deterioration of creditquality of loan portfolios to companies in a given NACE sector(manufacturing in DE) imposing 5% PD and 50% LGD

“Spectral” graph shows impact of the contagion losses of 500+ banks(the darker the bar, the higher the fraction of capital wiped out bycontagion)


Figure 8: Contagion simulation for different deterioration of credit quality

5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 55% 60% 65% 70% 75% 80% 85% 90% 95%

AT DE DE DE DE DE DE DE DE DE DE DE DE DE DE DK DK ES ES FI FR GB GB GB GR IT IT IT NL NO PL SI

100%

Contagion mechanism – cascade triggered by a deterioration of credit qualityof loan portfolios to companies in a given NACE sector for (y-axis)PD ∈ {5%, 10%, . . . , 100%} and 50% LGD

“Spectral” graph of contagion losses of 500+ banks (the darker the bar, thehigher the fraction of capital wiped out by contagion)


Figure 9: Risk-weight policy impact on contagion triggered by deteriorationcredit quality

60%b

70%b

80%b

90%b

60%a

70%a

80%a


90%a

“Spectral” graph of contagion losses of 500+ banks (the darker the bar, thehigher the fraction of capital wiped out by contagion)

a) baseline case (PD∈ {60%, . . . , 90%})b) risk weights increased by a factor of 1.5 for all exposures to the

manufacturing sector in Germany


Figure 10: Defaults of banks in the cascade of contagion spreading triggered bylosses in the portfolio of loans to the manufacturing sector in DE

3%

5%

7%

9%

11%

13%

15%

17%

19%

21%

23%


25%

Defaults of banks triggered by banks failing to pay back their obligations asa result of losses related to decreasing credit quality of manufacturing loanportfolio in (counterfactual example!) Germany

Each bar indicates a defaulting bank under LE∈ {3%, 5%, . . . , 25%}Grzegorz Ha laj (ECB) Systemic Risk and Financial Networks, IPAM 26/03/2015 27 / 30

Figure 11: Second round defaults of banks in the cascade of contagion spreadingtriggered by losses in the portfolio of loans to the manufacturing sector in DE

3%

5%

7%

9%

11%

13%

15%

17%

19%

21%

23%


25%

Defaults of banks triggered by banks failing to pay back their obligations asa result of losses related to decreasing credit quality of manufacturing loanportfolio in GermanyEach bar indicates a defaulting bank only because their debtors defaultedunder LE∈ {3%, 5%, . . . , 25%}


Where may the predefined volumes of interbank assets andliabilities come from? Endogenous balance sheet


Conclusions

Endogenous interbank networks give an important insight into therole of banks’ investment and funding strategies in shaping theinterbank market and non-bank firms’ funding channels. The simple,mechanistic cascade models are too simplistic in assuming that banksdo not react to actions of other interbank participants and marketconditions.

It is easier to introduce heterogeneity of agents if the networkapproach is taken rather than macroeconomic (e.g. generalequilibrium) framework.

In the proposed framework, we are able to analyse different policymeasures addressing the systemic risk – their ultimate impact on themarket structure and efficiency in reducing the contagion risk.

Still, a more consistent clearing mechanism would be warranted.

The model needs to be calibrated to the observed interbank / lendingnetworks. How far are we from the truth? (Target 2 data to be used)


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