A summary of ongoing

research in SYRTO

project

SYstemic Risk TOmography:

Signals, Measurements, Transmission Channels, and Policy Interventions

Petros Dellaportas Athens University of Economics and Business - Department of Statistics Joint work with Arakelian, Plataniotis, Titsias, Savona, Vrontos SYRTO Code Workshop Workshop on Systemic Risk Policy Issues for SYRTO July, 2 2014 - Frankfurt (Bundesbank-ECB-ESRB)

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Description of the data5-year sovereign CDS of 7 countries in the euro area: France, Germany, Greece, Ireland,

Italy, Portugal and Spain.

Indices of banking and financial sector in Europe

dates: January 1, 2008 to October 7, 2013.

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

CDS -all countries

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

0.5

1

1.5

2

2.5

x 104

FranceGermanyGreeceIrelandItalyPortugalSpainUS

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

CDS -all countries without Greece

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

200

400

600

800

1000

1200

1400

1600

FranceGermanyIrelandItalyPortugalSpainUS

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

CDS - Greece

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

0.5

1

1.5

2

2.5

x 104

Greece

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Dependencies via copulasFor every pair of instruments we use the modelling approach of Arakelian and Dellaportas

and construct a non-parametric estimate of their dependence (Kendal τ ) across time

this requires a computer-intensive parallel reversible jump MCMC algorithm for every pair

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Greece

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

0

0.1

0.2

0.3

0.4

0.5

0.6

GrGerGrFrGrIrGrItGrPortGrSp

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Spain

2008 2009 2010 2012 2013

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

SpFrSpGerSpGrSpIrSpItSpPort

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Germany

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

0.1

0.2

0.3

0.4

0.5

0.6

GerFrGerGrGerIrGerItGerPortGerSp

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Italy

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

ItFrItGerItGrItIrItPortItSp

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Ireland

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

0.1

0.2

0.3

0.4

0.5

0.6

0.7

IrGrIrGerIrFrIrItIrPortIrSp

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Portugal

04/02/08 08/15/09 12/28/10 05/11/12 09/23/13

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

PortFrPortGerPortGrPortIrPortItPortSp

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Current researchTreat all bivariate dependencies (estimated Kendal τ ’s) as time

series

Investigate forecasting and dependencies

possible avenue: Bayesian factor models. The assumption of

normal errors in the response is obviously wrong so we need

some clever modelling. Factors could be

dependencies between Greece-Portugal-Ireland

dependencies between Germany-France-Italy-Spain

dependencies between the bank and financial indices

inter-dependencies between the groups above

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Description of the data600 stocks from European index

Available stock information (sector, market)

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

Dynamic eigenvalue and eigenvector modellingWe decompose the covariance matrix at time t Σt = PtΛt PT

t and model Λt and Pt with an

AR(1) process.

Since Pt is a rotation matrix, it can be parameterised w.r.t. N(N − 1)/2 Givens angles, each

one belonging to matrix Gjt:

Pt =

N(N−1)2∏

j=1

Gjt

The problem depends on a a very demanding MCMC algorithm. It works well with some very

efficient proposal densities.

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

A factor model that reduces the dimension of the problem

yt = Lft + εt , εt ∼ N (0, σ2IN )

where yt ∈ RN is the vector of log returns at time t , L ∈ RN×K is a sparse fixed matrix of factor

loadings. L may consist of dummy variables that specify sectors and countries. The latent variable

ft ∈ RK follows the MSV model, i.e.

ft ∼ N (0,Σt )

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

The model

r jit = aj

i + bjit v

jt + ej

it

bjit = bj

0i + φji (bj

it−1 − bj0i ) + A′Gj

t + µjit

v jt = aj

0 + aj1Vt + ω

jt

Vt = B′Xt + ut

j sectors (Sovereign, Banks and FinancialIntermediaries, Corporations)

i financial assets (CDs and equity returns)

r: returns

v: sector systemic risk

G,X: covariates

V: macro-systemic risk factor

Model 1: Copulas Model 2: Multivariate Stochastic volatility Model 3: A Bayesian factor model Model 4: Probability of Bank defaults

The modeluse of balance sheets and market data of bank stocks of the European index

calculate financial ratios and estimate the debt of the bank

Use the multivariate stochastic volatility model above

Estimate the probability that the Asset value is smaller than the debt

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.