Bank Interconnectedness

What determines the

links?

SYstemic Risk TOmography:

Signals, Measurements, Transmission Channels, and Policy Interventions

Puriya Abbassi, Natalia Podlich Deutsche Bundesbank Christian Brownlees, Christina Hans Universitat Pompeu Fabra SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO July, 2 2014 - Frankfurt (Bundesbank-ECB-ESRB)

Introduction Data Model Estimation Empirical Results Conclusion

Bank Interconnectedness

What determines the links?

Puriya Abbassi† Christian Brownlees‡

Christina Hans‡ Natalia Podlich†

† Deutsche Bundesbank

‡Universitat Pompeu Fabra

02.07.2014

Introduction Data Model Estimation Empirical Results Conclusion

Motivation

• Modelling network structures has become increasinglyimportant both for researchers and for policy makers toassess the potential of contagion in the financial system

• Which network configuration is more dangerous for thefinancial system?

●

●

dgz

blb

lbb

hsh

lht

nlbwlb

dzb

wgz

dba

uni

K2006−12−31

●●

●

blblbb

hsh

lht

wgz

dba

com

uni

K2005−12−31

dgz

lbw

blb

lbb

hsh

lht

nlb

wlb

dzb

wgz

dba

com

uni

K2007−12−31

●●

●

blblbb

hsh

lht

wgz

dba

com

uni

K2005−12−31

●

dgz

lbw

blb

lbb

hsh

lht

nlb

wlb

dzb

wgz

dba

com

uni

K2008−12−31

Introduction Data Model Estimation Empirical Results Conclusion

Motivation

• Modelling network structures has become increasinglyimportant both for researchers and for policy makers toassess the potential of contagion in the financial system

Quarter 4, 2006 Quarter 4, 2007 Quarter 4, 2008

●

●

dgz

blb

lbb

hsh

lht

nlbwlb

dzb

wgz

dba

uni

K2006−12−31

●●

●

blblbb

hsh

lht

wgz

dba

com

uni

K2005−12−31

dgz

lbw

blb

lbb

hsh

lht

nlb

wlb

dzb

wgz

dba

com

uni

K2007−12−31

●●

●

blblbb

hsh

lht

wgz

dba

com

uni

K2005−12−31

●

dgz

lbw

blb

lbb

hsh

lht

nlb

wlb

dzb

wgz

dba

com

uni

K2008−12−31

Introduction Data Model Estimation Empirical Results Conclusion

Motivation

• Approaches to compute interconnectedness from marketdata are widely used in order to assess financial stabilityand systemic default probability

• But: what is the relation between perceived connectivityimplied by the market and fundamental channels?

• Data on networks through e.g. interbank lending orasset commonality is confidential or not available

• The information reflected by networks based on publiclyavailable data is unclear

Introduction Data Model Estimation Empirical Results Conclusion

Motivation

• Efficient market hypothesis: financial markets areinformationally efficient, and prices contain all availableinformation

• Question: What is the information content of networkscomputed using market data? Do they reflect

• Direct connections through bilateral exposures• Indirect connections through commonalities• Information contagion

...or not fundamentally driven market expectations?

Introduction Data Model Estimation Empirical Results Conclusion

Idea of this work

• Central questions:• What is the relation between networks based on publicly

available data and fundamental channels ofinterconnectedness?

• What is the information content of the time-varyingcomponent?

Introduction Data Model Estimation Empirical Results Conclusion

Idea of this work

• Our approach:• Model network structures for a sample of German banks

based on CDS data

• Compare their information content to two fundamentalchannels:

• Direct connections through interbank exposures

• Indirect connections through common exposures tosimilar asset classes

Introduction Data Model Estimation Empirical Results Conclusion

Roadmap

1. Overview of related literature

2. Data used in this study

3. Preliminary empirical findings

4. The way forward

Introduction Data Model Estimation Empirical Results Conclusion

Related literature

1. Networks based on market data• Billio, Getmansky, Lo & Pelizzon 2011 JFE - Granger Causality

Networks to determine structure of the financial system based on equityreturns

• Brownlees, Nualart & Hans 2014 WP - Credit Risk networkderived from idiosyncratic default intensities of banks based on CDS data

2. Interbank Lending Networks• Allen & Gale 2000 JPE - Theoretical model on financial contagion

through interbank markets• Iyer & Peydro 2009 - Empirical evidence for contagion through

interbank markets at the example of India

3. Interconnections through Asset Commonality• Allen, Babus & Carletti 2011 JFE - Theoretical model on

contagion effects through asset commonality• Caballero & Simsek 2013 JF - Theoretical model on fire sales in

complex environments

Introduction Data Model Estimation Empirical Results Conclusion

Data

• Our source for estimating credit risk networks: CDSspreads

• Bilateral swap agreements denoted in annualized basispoints

• Clean measure of credit risk of single institutions

• Total size of the CDS market in July 2007: $ 62.2 trillion

Introduction Data Model Estimation Empirical Results Conclusion

Data

• Sample of 13 large German banks

• CDS spreads of 1-year, 3-year, 5-year, 7-year and 10-yearmaturity for German sovereign and banks, daily frequency

• Riskless rate (Nelson-Siegel-Svensson curves)

• Interbank lending data from the Deutsche Bundesbankcredit register (all exposures > €1.5mio to financialfirms), quarterly frequency (confidential)

• Bank portfolio data, quarterly frequency (confidential)

• Sample period: October 1, 2005 - December 31, 2012

Descriptive Statistics

Introduction Data Model Estimation Empirical Results Conclusion

Credit Risk Model for CDS pricing

• Brownlees, Nualart & Hans 2014: Model for a panel offinancial entities building up on the standard reducedform framework for CDS pricing

• Default of single institutions can be triggered by twocomponents:

1. Systematic component (e.g. common macroeconomicshocks)

2. Idiosyncratic component with network structure (seeModel )

modelled as jumps of a Poisson process with stochasticintensity driven by a Brownian motion.

Introduction Data Model Estimation Empirical Results Conclusion

Credit Risk Model for CDS pricing

• The vector of Brownian Motions driving the idiosyncraticprocesses is allowed to have a covariance matrix

• The Bank Credit Risk Network is defined as a weighted,undirected graph, where two banks are connected iff theiridiosyncratic shocks are conditionally dependent.

• Hence, obtained linkages should reflect directbank-to-bank connections through various channels

Introduction Data Model Estimation Empirical Results Conclusion

Step 1: Estimating the Bank Credit Risk Network

1. We use a standard bootstrapping algorithm for strippingout perceived default intensities for both the sovereignand the 13 banks in our sample from CDS spreads.

2. We obtain idiosyncratic default intensities for all banks byfiltering out the systematic influence.

3. We estimate the structure of the bank credit risk networkas partial correlations among those, and use LASSO typeestimation for recovering the sparsity structure of thenetwork.

LASSO

Introduction Data Model Estimation Empirical Results Conclusion

Step 2: Judging the determinants

We take the bank credit risk network estimated on a quarterlybasis and assess the impact of both direct and indirectchannels of interconnectedness by estimating

ρijt = β0 + β1Iijt + β2Dijt + β3Cijt−1 + αt + γij + εijt

where

• ρijt is the partial correlation according to our model

• Iijt denotes the interbank exposure

• Dijt is a measure of portfolio distance

• Cijt−1 is a set of back-dated pair-wise control variables

between banks i and j at time t.

Introduction Data Model Estimation Empirical Results Conclusion

Preliminary Results

• Roughly 15 % of the variation in the partial correlationnetwork can be attributed to bank-pair information

• Approach to capture bank-to-bank component:• Interbank exposures• Common risk exposures

Introduction Data Model Estimation Empirical Results Conclusion

Preliminary Results

Interbank Exposures:

• Low explanatory power per se, in line with previousliterature: if interbank lending network is complete, it isrobust to shocks (Allen & Gale 2000)

• Interbank exposures relative to a bank’s Core Tier 1Capital: the higher interbank exposures with respect tocapital, the higher the partial correlations

• The effect is non-linear and stronger when the lossabsorption capacity is small

Introduction Data Model Estimation Empirical Results Conclusion

Preliminary Results

Common Risk Exposures:

• Portfolio similarity of two banks (Cai, Saunders & Steffen2014):

Dijt =

√√√√ A∑a=1

(wiat − wjat)2

where wiat is the relative portfolio weight along threedimensions

• Weak overall significance

• Stronger effects if we focus on troubled asset classes

Introduction Data Model Estimation Empirical Results Conclusion

Preliminary Results

What about the remaining 85 %?

• Relationships through fundamental channels are generallymore persistent and rigid over time relative to CDS pricedevelopments

• Amplification mechanism might differ across and withinthe financial and sovereign crisis

• Market expectations might not be fundamentally driven(market sentiment, ’too big to fail’)

Introduction Data Model Estimation Empirical Results Conclusion

Concluding remarks / The way forward

• We build up on a model estimating credit riskconnections in a panel of financial entities based on CDSdata, and compare its outcomes to two fundamentalchannels: interbank exposures and asset commonality

• We find that the information content of networksobtained with market data reflects both direct andindirect channels of interconnectedness, but there is alarge share left to be explained

• Next steps:• Increase sample of banks and richness of datasets• Use various ways to account for direct and indirect

channels (e.g. dependence on wholesale funding)• ...

Appendix A Appendix B Appendix C

List of banks in the sample

Category Name of the institution Abbreviation

Privatbanken Deutsche Bank AG DBACommerzbank AG COMUnicredit AG UNI

Landesbanken DekaBank Deutsche Girozentrale DGZHSH Nordbank HSHLandesbank Baden-Wurttemberg LBWBayerische Landesbank BLBLandesbank Berlin LBBLandesbank Hessen - Thuhringen LHTNorddeutsche Landesbank NLBWest LB / Portigon AG WLB

Genossenschaftsbanken DZ Bank DZBWGZ Bank AG WGZ

Appendix A Appendix B Appendix C

Quantile statistics for 5-year bank CDS spreads

Mean Std. Dev. Min. Median Max.DGZ 66.77 42.42 5.93 69.27 192.08LBW 100.81 72.15 5.62 103.5 346.07BLB 104.84 84.5 7.97 84.54 364.12LBB 89.36 59.55 8.92 92.51 317.8HSH 89.91 49.04 10.25 103.31 189.63LHT 69.97 41.72 7.92 69.9 155.8NLB 154.29 104.35 7 167.16 445.19WLB 102.79 64.47 7.29 119.19 259.97DZB 120.65 87.98 5.69 112.95 361.54WGZ 101.39 71.38 5.91 113.06 355.33DBA 103.21 69.45 5.95 116.33 302.56COM 48.55 26.04 5.63 50.93 125.64UNI 99.38 68.91 5.77 109.97 334.66

back to Data

Appendix A Appendix B Appendix C

Tibshirani 1996: LASSO

• Regression representation:

Bi(t) =∑j 6=i

βijBj(t) + ui(t)

with ui(t) ∼ N (0, tkii

) and βij = ρij√

kjjkii

• Estimate parameters as well as select and estimate thepartial correlations by minizing the following objectivefunction

ρ = minρij

∑i

∑t

[sit − sit ]2 + θ

∑j 6=i

|ρij |

based on pre–estimators of kii i = 1, ..., n

back to Model

Appendix A Appendix B Appendix C

Credit Risk Model for CDS pricing

• We develop a model for a panel of n financial entities,where default of single institutions can be triggered by

1. Systematic component

2. Idiosyncratic component

• We use the model to derive closed form CDS prices

Appendix A Appendix B Appendix C

Systematic component

• We model systematic shocks as jumps of a Poissonprocess M(t) with intensity λ

dλ(t) = a(m − λ(t))dt + b√λ(t)dW (t)

where W (t) is a Brownian motion

• Each of the i = 1, ..., n entities has a conditional defaultprobability γi following a systematic shock

Appendix A Appendix B Appendix C

Idiosyncratic component

• We model an idiosyncratic shock as the first jump ofPoisson process Ni(t) with intensity ξi

dξi(t) = αi(µi − ξi(t))dt +√ξi(t)dBi(t)

where Bi(t) are Brownian motions independent of W (t)

• We assume that B(t) = (B1(t), ...,Bn(t)) is a correlatedBrownian motion with covariance matrix Σ, where weconstrain Σ to allow for a network structure among theBi ’s

Appendix A Appendix B Appendix C

Bank Credit Risk Network

• We define the network of bank interconnections as anundirected graph N = (V , E) where V = 1, ..., n is the setof banks and E ⊂ V × V is the set of edges

• We define two banks to be connected by an edge iff theiridiosyncratic default shocks are conditionally dependent,i.e.

∀(i , j) ∈ E Bi(t) 6⊥ Bj(t) | Bk(t) ∀k 6= i , j

Appendix A Appendix B Appendix C

Bank Credit Risk Network

• We can equivalently characterize the network betweenidiosyncratic default shocks using the concentrationmatrix K = Σ−1 with entries kij

• Then two banks are conditionally independent iff kij = 0

Bi(t) ⊥ Bj(t) | Bk(t) ∀k 6= i , j ⇔ kij = 0,

in other words, E = {(i , j) : kij 6= 0}

• Important implication: We can reformulate the problemof estimating the Bank Credit Risk Network as theproblem of estimating a sparse concentration matrix

Appendix A Appendix B Appendix C

Instantaneous probability of default

Bank default probability:

P (no default occurs by time t)

= P(Ni (t) = 0)∞∑j=0

P(M(t) = j)(1− γi )j

= exp

(−∫ t

0ξi (s)ds

) ∞∑j=0

1

j!exp(−

∫ t

0λ(s)ds)

((1− γi )

∫ t

0λ(s)ds

)j

= exp

(−∫ t

0(γiλ(s) + ξi (s))ds

)

Appendix A Appendix B Appendix C

Pricing CDS

Standard framework for valuing credit derivatives(Duffie & Singleton 1999)

Protection leg of a CDS contract:

CDSpi ro = EQ

(∫ T

0

exp

[−∫ t

0

(r(s) + γiλ(s) + ξi(s))(1− ω)ds

]dt

)

Premium leg of a CDS contract:

CDSpi re = EQ

(si

∫ T

0

exp

[−∫ t

0

(r(s) + γiλ(s) + ξi(s))ds

]dt

)

Appendix A Appendix B Appendix C

Pricing CDS

For no arbitrage:CDSpro

i = CDSprei ,

hence

si =ωEQ

(∫ T

0D(t)(γiλ(s) + ξi(s)) exp

[−∫ t

0(γiλ(s) + ξi(s))ds

]dt)

EQ(∫ T

0D(t) exp

[−∫ t

0(γiλ(s) + ξi(s))ds

]dt)

=ω∫ T

0D(t)

(F i(λ(0), t)H(ξi(0), t) + γiG (ξi(0), t)I i(λ(0), t)

)dt∫ T

0(D(t)F i(λ(0), t)G (ξi(0)) dt

Appendix A Appendix B Appendix C

Closed Form Solution

F i(λ(0), t) = F1(t) exp(F2(t)λ(0))

G (ξi(0), t) = G1(t) exp(G2(t)ξi(0))

H(ξi(0), t) = (H1(t) + H2(t)ξi(0)) exp(G2(t)ξi(0))

I i(λ(0), t) = (I1(t) + I2(t)λ(0)) exp(F2(t)λ(0))

Appendix A Appendix B Appendix C

F1(t) = exp

(−am(a − ψi )t

b2

)(νi − 1

νi − etψi

) 2amb2

F2(t) =a − ψi

b2−

2ψi etψi

b2(νi − etψi )

G1(t) = exp

(−αiµi (αi − Φi )t

Γ2i

)(θi − 1

θi − etΦi

) 2αiµiΓ2i

G2(t) =α− Φi

Γ2i

−2Φi e

tΦi

Γ2i (θi − etΦi )

H1(t) =αiµi

Φi

(eΦi t − 1) exp

(−αiµi (αi − Φi )t

Γ2

)(θi − 1

θi − eΦi t

) 2αiµiΓ2i

+1

H2(t) = exp

(−αiµi (αi − Φi )t

Γ2i

+ Φi t

)(θi − 1

θi − eΦi t

) 2αiµiΓ2i

+2

Appendix A Appendix B Appendix C

I1(t) =am

ψi

(eψi t − 1) exp

(−am(a − ψi )t

b2

)(νi − 1

ν − eψi t

) 2amb2 +1

I2(t) = exp

(−am(a − ψi )t

b2+ ψi t

)(νi − 1

νi − eψi t

) 2amb2 +2

with

ψi =√

a2 + 2γi b2

νi =a + ψi

a − ψi

Φi =√α2i + 2Γ2

i

θi =αi + Φi

αi − Φi

Γ2i =

∑j 6=i,k 6=i

βijβikσjk +

1

kii

βij = ρij

√kjj

kii.

back to Model

This project has received funding from the European Union’s

Seventh Framework Programme for research, technological

development and demonstration under grant agreement n° 320270

www.syrtoproject.eu

This document reflects only the author’s views.

The European Union is not liable for any use that may be made of the information contained therein.