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Spillover Dynamics for Systemic Risk Measurement Using Spatial Financial Time Series Models SYstemic Risk TOmography: Signals, Measurements, Transmission Channels, and Policy Interventions Francisco Blasques (a,b) Siem Jan Koopman (a,b,c) Andre Lucas (a,b) Julia Schaumburg (a,b) (a) VU University Amsterdam (b) Tinbergen Institute (c) CREATES ESEM Toulouse, August 25-29, 2014

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Page 1: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Spillover Dynamics for Systemic Risk Measurement Using Spatial Financial Time Series Models

SYstemic Risk TOmography:

Signals, Measurements, Transmission Channels, and Policy Interventions

Francisco Blasques (a,b)

Siem Jan Koopman (a,b,c) Andre Lucas (a,b) Julia Schaumburg (a,b) (a)VU University Amsterdam (b)Tinbergen Institute (c)CREATES

ESEM Toulouse, August 25-29, 2014

Page 2: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

This project has received funding from the European Union’s

Seventh Framework Programme for research, technological

development and demonstration under grant agreement no° 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.

Page 3: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Introduction 3

Measuring systemic sovereign credit risk

Systemic risk: Breakdown risk of thefinancial system, induced by theinterdependence of its constituents.

European sovereign debt since 2009:

I Strong increases and comovements of credit spreads.

I Financial interconnectedness across borders due to mutual

borrowing and lending + bailout engagements.

⇒ Spillovers of shocks between member states.

⇒ Unstable environment: need for time-varying parameter models andfat tails.

Spillover Dynamics

Page 4: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Introduction 3

Measuring systemic sovereign credit risk

Systemic risk: Breakdown risk of thefinancial system, induced by theinterdependence of its constituents.

European sovereign debt since 2009:

I Strong increases and comovements of credit spreads.

I Financial interconnectedness across borders due to mutual

borrowing and lending + bailout engagements.

⇒ Spillovers of shocks between member states.

⇒ Unstable environment: need for time-varying parameter models andfat tails.

Spillover Dynamics

Page 5: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Introduction 3

Measuring systemic sovereign credit risk

Systemic risk: Breakdown risk of thefinancial system, induced by theinterdependence of its constituents.

European sovereign debt since 2009:

I Strong increases and comovements of credit spreads.

I Financial interconnectedness across borders due to mutual

borrowing and lending + bailout engagements.

⇒ Spillovers of shocks between member states.

⇒ Unstable environment: need for time-varying parameter models andfat tails.

Spillover Dynamics

Page 6: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Introduction 4

This project

I New parsimonious model for overall time-varying strength ofcross-sectional spillovers in credit spreads (systemic risk).⇒ Useful for flexible monitoring of policy measure effects.

I Extension of widely used spatial lag model to generalizedautoregressive score (GAS) dynamics and fat tails in financial data.

I Asymptotic theory and assessment of finite sample performance ofthis ’Spatial GAS model’.

Spillover Dynamics

Page 7: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Introduction 5

European sovereign systemic risk 2009-2014

Mario Draghi: „Whatever it takes“

Ireland bailed out Help offer to Greece

First LTRO Second LTRO

ESM inaugurated

Greece : record deficit

New supervisory authority

Spillover Dynamics

Page 8: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Introduction 6

Some related literature

I Systemic risk in sovereign credit markets:

. Ang/Longstaff (2013), Lucas/Schwaab/Zhang (2013),

Ait-Sahalia/Laeven/Pelizzon (2014), Aretzki/Candelon/Sy (2011),

Kalbaska/Gatkowski (2012), De Santis (2012), Caporin et al. (2014),

Korte/Steffen (2013), Kallestrup/Lando/Murgoci (2013), Beetsma et al.

(2013, 2014).

I Spatial econometrics:

. General: Cliff/Ord (1973), Anselin (1988), Cressie (1993), LeSage/Pace(2009), Ord (1975), Lee (2004), Elhorst (2003);

. Panel data: Kelejian/Prucha (2010), Yu/de Jong/Lee (2008, 2012),Baltagi et al. (2007, 2013), Kapoor/Kelejian/Prucha (2007);

. Empirical finance: Keiler/Eder (2013), Fernandez (2011),

Asgarian/Hess/Liu (2013), Arnold/Stahlberg/Wied (2013), Wied (2012),

Denbee/Julliard/Li/Yuan (2013), Saldias (2013).

Spillover Dynamics

Page 9: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Spatial GAS model 7

Spatial lag model for panel data

yi,t = ρt

n∑j=1

wijyj,t +K∑

k=1

xik,tβk + ei,t , ei,t ∼ tν(0, σ2)

where

I |ρt | < 1 is time-varying spatial dependence parameter,

I wij , j = 1, ..., n, are nonstochastic spatial weights adding up to one with wii = 0,

I xik,t , k = 1, ...,K are individual-specific regressors,

I βk , k = 1, ...,K , σ2 and ν are unknown coefficients.

Matrix notation:

yt = ρt Wyt︸︷︷︸’spatial lag’

+Xtβ + et or

yt = ZtXtβ + Ztet , with Zt = (In − ρtW )−1.

⇒ Model is highly nonlinear and captures feedback.

Spillover Dynamics

Page 10: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Spatial GAS model 7

Spatial lag model for panel data

yi,t = ρt

n∑j=1

wijyj,t +K∑

k=1

xik,tβk + ei,t , ei,t ∼ tν(0, σ2)

where

I |ρt | < 1 is time-varying spatial dependence parameter,

I wij , j = 1, ..., n, are nonstochastic spatial weights adding up to one with wii = 0,

I xik,t , k = 1, ...,K are individual-specific regressors,

I βk , k = 1, ...,K , σ2 and ν are unknown coefficients.

Matrix notation:

yt = ρt Wyt︸︷︷︸’spatial lag’

+Xtβ + et or

yt = ZtXtβ + Ztet , with Zt = (In − ρtW )−1.

⇒ Model is highly nonlinear and captures feedback.

Spillover Dynamics

Page 11: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Spatial GAS model 8

GAS dynamics for ρt

I Reparameterization: ρt = h(ft) = tanh(ft).

I ft is assumed to follow a dynamic process,

ft+1 = ω + ast + bft ,

where ω, a, b are unknown parameters.

I We specify st as the first derivative (“score”) of the predictive likelihoodw.r.t. ft (Creal/Koopman/Lucas, 2013).

I Model can be estimated straightforwardly by maximum likelihood (ML).

I For theory and empirics on different GAS/DCS models, see also, e.g.,Creal/Koopman/Lucas (2011), Harvey (2013), Harvey/Luati (2014),Blasques/Koopman/Lucas (2012, 2014a, 2014b).

Spillover Dynamics

Page 12: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Spatial GAS model 9

Score

Score for Spatial GAS model with normal errors:

st =

((1 + n

ν)y ′tW

′Σ−1(yt − h(ft)Wyt − Xtβ)

1 + 1ν

(yt − h(ft)Wyt − Xtβ)′Σ−1(yt − h(ft)Wyt − Xtβ)− tr(ZtW )

)· h′(ft)

Spillover Dynamics

Page 13: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Spatial GAS model 10

Score

Score for Spatial GAS model with t-errors:

st =

((1 + n

ν)y ′tW

′Σ−1(yt − h(ft)Wyt − Xtβ)

1 + 1ν

(yt − h(ft)Wyt − Xtβ)′Σ−1(yt − h(ft)Wyt − Xtβ)− tr(ZtW )

)· h′(ft)

Spillover Dynamics

Page 14: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Theory 11

Theory for Spatial GAS model

I Extension of theoretical results on GAS models inBlasques/Koopman/Lucas (2014a, 2014b).

I Nonstandard due to nonlinearity of the model, particularly in thecase of Spatial GAS-t specification.

I Conditions:

. moment conditions;

. b + a ∂st∂ftis contracting on average.

I Result: strong consistency and asymptotic normality of MLestimator.

I Also: Optimality results (see paper).

Spillover Dynamics

Page 15: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Simulation 12

Simulation results (n = 9, T = 500)

0 100 200 300 400 500

0.0

0.4

0.8

Sine, dense W, t−errorsrh

o.t

0 100 200 300 400 500

0.0

0.2

0.4

0.6

0.8

1.0

Step, dense W, t−errors

rho.

t

Spillover Dynamics

Page 16: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 13

Systemic risk in European credit spreads:Data

I Daily log changes in CDS spreads from February 2, 2009 - May 12,2014 (1375 observations).

I 8 European countries: Belgium, France, Germany, Ireland, Italy,Netherlands, Portugal, Spain.

I Country-specific covariates (lags):

. returns from leading stock indices,

. changes in 10-year government bond yields.

I Europe-wide control variables (lags):

. term spread: difference between three-month Euribor and EONIA,

. change in volatility index VSTOXX.

Spillover Dynamics

Page 17: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 14

Five European sovereign CDS spreads

2009 2010 2011 2012 2013 2014

200

400

600

800

1000

1200

spre

ad (

bp)

IrelandSpainBelgiumFranceGermany

average correlation of log changes = 0.65

Spillover Dynamics

Page 18: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 15

Spatial weights matrix

I Idea: Sovereign credit risk spreads are (partly) driven by cross-border debtinterconnections of financial sectors (see, e.g. Korte/Steffen (2013),Kallestrup et al. (2013)).

I Intuition: European banks are not required to hold capital buffers againstEU member states’ debt (’zero risk weight’).

I If sovereign credit risk materializes, banks become undercapitalized, sothat bailouts by domestic governments are likely, affecting their creditquality.

I Entries of W : Three categories (high - medium - low) of cross-border

exposures in 2008.∗

∗Source: Bank for International Settlements statistics, Table 9B: International

bank claims, consolidated - immediate borrower basis.

Spillover Dynamics

Page 19: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 16

Empirical model specifications

model mean equation errors et ∼

(0, σ2In) (0,Σt)

Static spatial yt = ρWyt + Xtβ + et N, t

Sp. GAS yt = h(f ρt )Wyt + Xtβ + et N, t t

Sp. GAS+mean fct. yt = ZtXtβ + λf λt + Ztet t

Benchmark yt = Xtβ + λf λt + et t

Spillover Dynamics

Page 20: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 17

Model fit comparison

Static spatial Time-varying spatial

et ∼ N(0, σ2In) tν(0, σ2In) N(0, σ2In) tν(0, σ2In)

logL -26396.63 -24574.48 -26244.45 -24506.11

AICc 52807.35 49165.06 52507.03 49032.39

Time-varying spatial-t Benchmark-t

(+tv. volas) (+mean f.+tv.volas) (+mean f.+tv.volas)

logL -24175.70 -24156.96 -26936.15

AICc 48389.97 48375.30 53927.42

Spillover Dynamics

Page 21: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 18

Parameter estimates

I Spatial dependence is high and significant.

I Spatial GAS parameters:

. High persistence of dynamic factors reflected by largeestimates for b.

. Estimates for score impact parameters a are small butsignificant.

I Estimates for β have expected signs.

I Mean factor loadings:

. Positive for Ireland, Portugal, Spain.

. Negative for Belgium, France, Germany, Netherlands, Italy.

Spillover Dynamics

Page 22: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 19

Different choices of W

Candidates (all row-normalized):

I Raw exposure data (constant): Wraw

I Raw exposure data (updated quarterly): Wdyn

I Three categories of exposure amounts (high, medium, low): Wcat

I Geographical neighborhood (binary, symmetric): Wgeo

Model fit comparison (only t-GAS model):

Wraw Wdyn Wcat Wgeo

logL -24745.56 -24679.44 -24506.11 -25556.85

Parameter estimates are robust.

Spillover Dynamics

Page 23: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 19

Different choices of W

Candidates (all row-normalized):

I Raw exposure data (constant): Wraw

I Raw exposure data (updated quarterly): Wdyn

I Three categories of exposure amounts (high, medium, low): Wcat

I Geographical neighborhood (binary, symmetric): Wgeo

Model fit comparison (only t-GAS model):

Wraw Wdyn Wcat Wgeo

logL -24745.56 -24679.44 -24506.11 -25556.85

Parameter estimates are robust.

Spillover Dynamics

Page 24: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Application 20

Spillover strength 2009-2014

Mario Draghi: „Whatever it takes“

Ireland bailed out Help offer to Greece

First LTRO Second LTRO

ESM inaugurated

Greece : record deficit

New supervisory authority

Spillover Dynamics

Page 25: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Conclusions 21

Conclusions

I Spatial model with dynamic spillover strength and fat tails isnew, and it works (theory, simulation, empirics).

I European sovereign CDS spreads are strongly spatiallydependent.

I Decrease of systemic risk from mid-2012 onwards; possiblydue to EU governments’ and ECB’s bailout measures.

I Best model: Time-varying spatial dependence based ont-distributed errors, time-varying volatilities, additional meanfactor, and categorical spatial weights.

Spillover Dynamics

Page 26: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Thank you.

Page 27: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Appendix 23

Model specifications (t-errors)I individual variance factors

. Σt = Σ(fσt ) = diag(exp(f σ1t ), ..., exp(f σnt ))

. fσt+1 = ωσ + asσt + bfσt , with

sσt =

− 1

2− ν+n

1ν exp(fσ

t,1)·(yt,1−h(f

ρt )

∑nj=1 w1j yt,j−x′t,1β)2

1+ 1ν

(yt−h(fρt )Wyt−Xtβ)′Σ(fσt )−1(yt−h(f

ρt )Wyt−Xtβ)

...

− 12− ν+n

1ν exp(fσt,n)

·(yt,n−h(fρt )

∑nj=1 wnj yt,j−x′t,nβ)2

1+ 1ν

(yt−h(fρt )Wyt−Xtβ)′Σ(fσt )−1(yt−h(f

ρt )Wyt−Xtβ)

I mean factor

. factor loadings: λ = (λ1, ..., λn)′

. f λt+1 = ωλ + aλsλ + bλf λt with

sλt =(1 + n

ν)(Z−1

t λ)′Σ−1et

1 + 1νe′tΣ−1et

, et = yt − h(f ρt )Wyt − Xtβ − Z−1t λf λt

Spillover Dynamics

Page 28: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Appendix 24

Estimation results: Full model

ωλ -0.0012 ωσ1 Belgium 0.0426 ω 0.0307(0.0252) (0.0125) (0.0229)

Aλ 0.3494 ωσ2 France 0.0448 A 0.019(0.8937) (0.0142) (0.007)

Bλ 0.6891 ωσ3 Germany 0.0573 B 0.9636(0.1065) (0.0155) (0.0271)

λ1 Belgium -0.2776 ωσ4 Ireland 0.0301 const. -0.0621(0.2308) (0.01) (0.024)

λ2 France -0.2846 ωσ5 Italy 0.0471 VStoxx -0.0257(0.3137) (0.0136) (0.0157)

λ3 Germany -0.2029 ωσ6 Netherlands 0.0443 term sp. 0.0693(0.2811) (0.0132) (0.0705)

λ4 Ireland 0.405 ωσ7 Portugal 0.0524 stocks -0.102(0.6928) (0.0153) (0.0183)

λ5 Italy -0.1604 ωσ8 Spain 0.0591 yields 0.0173(0.2429) (0.016) (0.0026)

λ6 Netherlands -0.1891 Aσ 0.1826 λ0 3.1357(0.2519) (0.023) (0.1977)

λ7 Portugal 0.4614 Bσ 0.9479(0.8334) (0.0135)

λ8 Spain 0.0988 logLik -24156.96(0.3635) AICc 48375.3

Spillover Dynamics

Page 29: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Appendix 25

Basic model: filtered GAS parameter

2009 2010 2011 2012 2013 2014

0.4

0.5

0.6

0.7

0.8

0.9

rho_

t

t−GAS modelnormal−GAS model

Spillover Dynamics

Page 30: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Appendix 26

Filtered parameter: Full vs. basic model

2009 2010 2011 2012 2013 2014

0.4

0.5

0.6

0.7

0.8

0.9

rho_

t

basic t−GAS modelfull t−GAS model

I Neglecting heteroskedasticity and common mean dynamics leads toslightly biased filtered process.

Spillover Dynamics

Page 31: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Appendix 27

Residual diagnostics: Full model

Test for remaining autocorrelation and ARCH effects in standardized residualsfrom full model (Spatial GAS+volas+mean factor)

sovereign LB test stat. ARCH LM test stat. average cross-corr.raw residuals raw residuals raw residuals

Belgium 108.64 15.93 169.91 25.53 0.70 0.07France 49.48 30.42 160.44 43.32∗ 0.66 -0.01Germany 62.61 19.49 142.70 53.78∗ 0.63 -0.07Ireland 129.89 17.53 302.23 87.11∗ 0.64 -0.07Italy 99.02 42.43∗ 102.13 150.88∗ 0.71 0.08Netherlands 55.69 33.29∗ 124.41 20.96 0.64 -0.05Portugal 167.91 32.56∗ 189.35 56.89∗ 0.65 0.03Spain 105.81 48.88∗ 253.68 154.42∗ 0.69 0.06∗Remaining effects at 5% level

Spillover Dynamics

Page 32: Spillover dynamics for sistemic risk measurement using spatial financial time series models. Julia Schaumburg, Andre Lucas, Siem Jan Koopman, and Francisco Blasques. Toulouse, August

Appendix 28

Simulation: Parameter tracking

I Data generating process:

yt = Ztet , et ∼ i .i .d .t5(0, In),

where Zt = (In − ρtW )−1, and t = 1, ..., 500.

I Weights matrix (row-normalized): cross-border debt of 9 Europeancountries (BIS data)

I Spatial dependence processes (Engle 2002):

1. Constant: ρt = 0.92. Sine: ρt = 0.5 + 0.4 cos(2πt/200)3. Fast sine: ρt = 0.5 + 0.4 cos(2πt/20)4. Step: ρt = 0.9− 0.5 ∗ I (t > T/2)5. Ramp: ρt = mod (t/200)

Spillover Dynamics