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,d) Julia Schaumburg (a,b)

(a)VU University Amsterdam (b)Tinbergen Institute (c)CREATES (d)Duisenberg School of Finance

Seventh Annual SoFiE Conference Toronto, June 11-13, 2014

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.

Introduction 3

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

Introduction 3

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

Introduction 3

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

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’.

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Introduction 5

European sovereign systemic risk 2009-2014

Draghi: „Whatever it takes“

Ireland bailed out

EU offers help to Greece

J.C. Trichet → M. Draghi

First LTRO Second LTRO

ESM starts operating

Greece : record deficit

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Introduction 6

Some related literature

I Systemic risk in sovereign credit markets:

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

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).

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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

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

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

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

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)

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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).

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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

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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 9 European countries: Belgium, France, Germany, Ireland, Italy,Netherlands, Portugal, Spain, United Kingdom.

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,

. interbank interest rate: change in three-month Euribor,

. change in volatility index VSTOXX.

Spillover Dynamics

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

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.

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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

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Application 17

Model fit comparison

Static spatial Spatial GAS

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

logL -29614.62 -27623.06 -29460.51 -27546.63

AICc 59245.35 55264.24 58941.19 55115.45

Spatial GAS-t Benchmark-t

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

logL -27174.94 -27153.83 -30161.63

AICc 54392.57 54354.47 60384.65

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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, Italy, Portugal, Spain.

. Negative for Belgium, France, Germany, Netherlands.

Spillover Dynamics

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 Exposures standardized by GDP: Wgdp

I Geographical neighborhood (binary, symmetric): Wgeo

Model fit comparison (only t-GAS model):

Wraw Wdyn Wcat Wgdp Wgeo

logL 27973.02 -27946.97 -27153.83 -27992.69 -28890.98

Parameter estimates are robust.

Spillover Dynamics

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 Exposures standardized by GDP: Wgdp

I Geographical neighborhood (binary, symmetric): Wgeo

Model fit comparison (only t-GAS model):

Wraw Wdyn Wcat Wgdp Wgeo

logL 27973.02 -27946.97 -27153.83 -27992.69 -28890.98

Parameter estimates are robust.

Spillover Dynamics

Application 20

Spillover strength 2009-2014

Mario Draghi: „Whatever it takes“

Ireland bailed out

EFSF established

Portugal bailed out

First LTRO Second LTRO

OMT program established

Greece : record deficit

Ireland exits bailout

Spain exits bailout

Spillover Dynamics

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.

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Thank you.