Modeling transmissions of volatility shocks: Application to CDS spreads during the euro area sovereign crisis.
Bellalah, Makram ; Bellalah, Mondher ; Boussada, Haifa 等
ABSTRACT
This paper tests empirically the contagion and the transmission
mechanism of shocks in volatility between the peripheral Eurozone
countries. We use the sovereign CDS spreads and the asymmetric model of
dynamic conditional correlation GARCH DCC. We investigate the effects of
positive and negative shocks over the long term. We investigate the
systemic nature of the crisis in Europe. We implement testing of the
non-linearity of propagation mechanisms of shocks through a long-term
interdependence VECM model (Johansen co-integration). The generated
results show that changes in the index of sovereign CDS have a very
significant effect on changes in stock indexes in Europe. This is
especially true in the case of Germany and France and the PIIGS
countries.
JEL Classifications: C5, G15
Keywords: sovereign debt crisis; DCC GARCH; cointegration;
transmission; volatility shocks
I. INTRODUCTION
In the last decade, adverse events have characterized the
international financial sphere and in particular the Europe. Indeed, the
subprime crisis had impacted financial markets in the world and also
Europe, which is seen as the most affected. In 2010, economists start
talking about a new outbreak of sovereign debt crisis in Greece. This
country shows a growth rate of 4.2% recorded from 2000 to 2007 and
became the most indebted country with a huge public debt reaching 152%
in 2011. Greece officially began to suffer from the crisis of sovereign
debt following the lowering of its sovereign credit rating.
The peripheral Eurozone countries have been affected following a
fault overpayment. Thus, a new risk adds to the global economy: the
sovereign debt crisis. This extends the global economy into recession,
coupled with serious political and social issues. Economists are
interested in studying the importance of contagion and its implications
for the stability of financial markets. Missio and Watzka (2011) have
estimated a model of dynamic conditional correlation (DCC) to analyze
the correlation structure of Greek, Portuguese, Spanish, Italian, Dutch,
Belgian and Austrian yield spreads bonds on the German yield study
contagion in the euro zone. Alter and Beyer (2014) presented an
empirical framework to quantify the spillovers. The study is based on
technical standards VAR generalized impulse response functions to
calculate the indices of infection in Spanish sovereign CDS shock. It
shows a high impact on both sovereign CDS in the euro zone and banks
during the first half of 2012 compared with 2011.
This article is based on an extension of this stream of the
literature and fits into the same perspective. The goal is to test
empirically the contagion as the transmission mechanism of shocks in
volatility between the peripheral countries of the euro area, based on
changes in sovereign CDS spreads. We analyze the transmission of shocks
to sovereigns in those markets for the same country indices. We refer in
the first time to the modeling of the conditional variance of GARCH
multi varied (MGARCH) to empirically test the contagion of sovereign
risk among the major countries of the European Union using sovereign CDS
spreads. This model has the flexibility of univariate GARCH models
associated with parsimonious parametric models for the correlations. The
model allows reduction through heteroscedasticity responsible for the
persistence of shocks to volatility and the overestimation of
cross-correlations.
We present the concept of systemic risk with an empirical test.
This allows to better understand its effects and testing transmission
market sovereign shock to the financial system of Europe, via the
cointegration model. Finally, we test the nonlinearity of propagation
mechanisms of shocks estimated through a model of long-term
interdependence VECM. The model is based on the cointegration test
(Johansen test).
II. SOVEREIGN DEBT: FROM CRISIS TO CRISIS:
Sovereign debt is defined by Cohen (2012) as "all debts held
by the State to its creditors who may be natural persons (companies,
banks, individuals, etc.), countries or other organizations (central
banks, Reserve Federal...) especially the one held in bonds denominated
in foreign currencies." The management of sovereign debt presents
economic aspects and political issues. Several states around the world
are plunged into a sovereign debt crisis following a bad management and
have been victims of significant consequences Western sovereign debt
crisis of 1980 led to political instability and crisis or war. The
Mexican crisis of 1982 affected Mexico, Brazil and Argentina. The crisis
in Argentina and the speculative attacks experienced by the Argentine
peso led to higher interest rates and unemployment, loss of confidence
and a rapid rise in public finances due to the increase in debt service.
In 2010, we observe a birth of another sovereign debt crisis in
Greece. It is observed as a direct effect of the subprime crisis, which
was triggered in the United States in 2007 and has particularly affected
Greece at its two main economic sectors: tourism and shipping. The
crisis emerge with the ECB decision to no longer accept bonds as
collateral for loans from private banks. The decision increases the risk
premium and the rates. The rescue plans adopted by the European Central
Bank includes among other things: accepting sovereign debt delisted,
putting bilateral loans amounting to 110 billion Euros, the
establishment of a European financial Stability Fund (EFSF) (750 billion
Euros) by the Ministers of finance the twenty-seven in 2010, setting a
new aid in 2001 to [euro] 110 billion from the IMF. The situation in
Greece worsens increasingly following a fault overpayment. The sovereign
debt crisis in Greece has quickly affected other peripheral countries of
the European Union, such as Italy whose debt reached 120% of GDP or
[euro] 1.9 trillion. Also, the crisis in Spain has tripped due to a
budget deficit of 11.2% recorded in 2010 and the deterioration of its
rating by the rating agency Standard and Poor's because of its low
growth prospects. For Ireland, the subprime crisis has severely affected
the banking sector. Then, a significant increase was observed in its
public deficit reaching 32% of GDP in 2011. The Portuguese crisis has
increased at the beginning of 2011, following a downgrade of its
sovereign debt rating of A+ to A- by Standard and Poor's. This
caused an increase in the borrowing rate. It is the fear of contagion
from the Greek crisis in the whole area that eventually cast doubt on
the sustainability of the euro. This is the goal of our next step to
review the literature on the effect of contagion.
III. THE CONTAGION EFFECT: DEFINITIONS AND LITERATURE REVIEW
Contagion attracted the attention of economists, politicians and
portfolio managers. Several theoretical and empirical works investigates
the crisis transmission mechanism. The crisis is considered as the
source of outbreak of some crises.
Pericoli and Sbracia (2003) defined contagion as "increasing
the probability of a crisis in a country with the advent of a crisis in
another country". This definition states that the contagion may
occur during financial turbulence when there is an increase in the
volatility of asset prices and extends from one market to another
market.
For Marais (2003), "contagion occurs when the volatility of
asset prices is spreading the crisis countries to other countries."
A simultaneous increase in volatility in different markets could be due
to normal interdependence between these markets or structural changes
affecting international markets links.
According to Forbes and Rigobon (2002), "contagion occurs when
cross-border co-movements in asset prices cannot be explained by
fundamentals." This definition focuses on the phenomenon of
contagion, which is identified by a significant increase in co-movements
of prices in markets after a crisis in a market or market group.
For Forbes and Rigobon (2002), "the shift-contagion occurs
when the transmission channel is growing or, more generally, changes
after a shock in a market." Contagion is considered a significant
increase links between financial markets due to a specific shock to a
country or group of countries. These links can be financial or real
(economic fundamentals) links or political ties (political relations
between countries)
A. Analysis of Unconditional Correlations of Sovereign CDS Spreads
in Europe
The objective of this section is to study the dynamics of
correlations between sovereign CDS. CDS are very important parameters
for investors all over the world. In fact, diversification strategies
for risk minimization depend essentially on correlations between those
assets. We will test the statistical significance of the increase in the
correlation coefficient between this and the quiet period as well as the
crisis based on sovereign CDS spreads of countries in the sample. We
show the significance of the impact of the Greek crisis to other
countries and the spread volatility contagion for the sovereign sector.
1. Data and methodology
The data is extracted from Bloomberg and Reuters. We use time
series of sovereign CDS spreads of the countries in the sample. The
study covers a period of nearly five years from 01 January 2008 to 31
December 2012, in daily frequency. These values are taken in basis
points. The following countries are used: the United Kingdom, France,
Germany, Italy, Greece, Spain, Portugal, Belgium, Sweden and Ireland.
The study covers a period of nearly five years in daily frequency, i.e.,
1,274 observations by markets. A selection of two sub-periods is done:
the quiet period that spans from 01/01/2008 to 14/01/2010 (i.e., 487
observations per country) and the crisis period, which runs from
15/01/2010 to 31/12/2012 (or 767 per country). This selection is based
on the date of the outbreak of sovereign debt crisis. These values are
taken in basis points.
2. Interpretations and results
The correlation coefficient is used to quantify this relationship
by the sign of the correlation (positive and negative) and by the
strength of this correlation. The interpretation of a correlation
coefficient depends on the context and on the objectives.
Following the decomposition of the total time in a quiet period and
a crisis period is the date of outbreak of sovereign debt crisis in
Greece. It is remarkable at the graphics and the correlation matrix that
almost all countries in the sample strongly correlate: the results range
from 0.6389 between Ireland-Finland to reach 0.9378 for France-Germany.
Denmark-Austria correlation is weak with other countries. The CDS spread
in Spain has the most pronounced correlation with all markets. We find
that the United Kingdom is highly correlated, but negative sign with the
majority of countries.
Figure 1 has witnessed a remarkable evolution of CDS spreads for
all countries in the sample for the period 2008-2009. This increase is
due to the impact of the subprime crisis and the increased risk of
bankruptcy or default on public debt. Following the bailout announced by
the IMF to reduce this risk, the trend has resumed at the end of 2009:
the spread level before the outbreak of the subprime crisis.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
During the crisis, the graphics of the evolution of sovereign CDS
spread in Figure 2 show a breakdown between the countries at the level
of the correlation matrix. Indeed, we note that the correlation
coefficients between the PUGS countries with France-Germany are steadier
in times of crisis than stable periods and decrease in Finland, Austria
and Sweden.
These findings indicate that the sovereign debt crisis in Greece is
quickly transmitted to the PUGS countries, but also to Germany and
France. The sovereign debt crisis had no significant impact on the
evolution of spread sovereign CDS in some countries as Austria and
Sweden, which has a relatively stable correlation with other countries
in the sample.
[FIGURE 2 OMITTED]
B. Asymmetric Dynamic Conditional Correlation Model (DCC-GARCH
(1.1)) of Sovereign CDS Spreads
To investigate empirically the effect of contagion from sovereign
debt crisis in Europe, we review a version of the multivariate GARCH
model: the model of dynamic conditional correlation (DCC) and via the
one estimated using the program WINRATS software (version 8.2). This
model was estimated in two steps. In the first step, we estimate the
univariate return series with a GARCH process. Then, in a second step,
we used the residuals of various multi-series to estimate the dynamic
correlations. This model is often preferred because it has the
flexibility of univariate GARCH processes and parsimony of parametric
estimation models of dynamic correlations. Thus, it can test the
volatility spillovers between countries in the sample. The analysis
allows demonstrating the significance of the impact of the Greek crisis
to other countries and the spreading volatility contagion for the
sovereign sector.
Several studies try to obtain reliable estimates of correlations of
assets over 20 years. The study of correlation is useful for the
detection of contagion via the transmission phenomena of volatility
shocks.
Bollerslev, Engle and Wooldridge (1988) introduced for the first
time, the concept of dynamic covariance. They used the GARCH multi
varied to calculate the dividend yield VTR functions in the risk premium
of the market. Engle and Sheppard (2001) introduced a new class of
models varied entitled "Models of conditional correlations."
The asymmetric DCC-GARCH model (1.1) is built on the idea of modeling
the conditional variances and correlations instead of simple modeling
conditional covariance matrix. The conditional covariance matrix is
decomposed into conditional standard deviations and correlation matrix :
[H.sub.t] = [D.sub.t] [R.sub.t] [D.sub.t], where [D.sub.t] = diagonal
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]: diagonal matrix of
conditional volatility of univariate GARCH models.
The information contained in [D.sub.t] are generated by the GARCH
(p, q) can be formulated as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)
where [R.sub.t]=[P.sub.ij,t,] which is the coefficient matrix of
conditional correlations varies over time. A is the square residues
delayed; and [beta] is the conditional variance delayed, w:asymmetric
term. The parameters ([alpha], [beta], w) of the DCC model are estimated
by the method of maximum likelihood.
Engle (2002) adopts a structure of GARCH in modeling the dynamics
of conditional correlations. Indeed, a DCC process of order (M, N) is
described as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
with [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], which is
the vector that contains the standardized residuals. [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] is the matrix of marginal
variance-covariance standard residues univariate models for each series
of asset returns. ([a.sub.m],[b.sub.n]) is the parameters that are
supposed to intercept, respectively, the effects of shocks and dynamic
correlations delayed on the contemporary level of the latter.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the diagonal
matrix containing the square root of the elements of the main diagonal
de [Q.sub.t].
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
The conditional correlation t is based on all information available
at t-1. Since it is based on the standardized residuals of the
univariate model, the conditional correlation matrix is nothing but the
matrix of conditional variance-covariance of the error terms.
The conditional correlation is written as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
Engle (2002) showed that the log-likelihood function can be
estimated as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
Note that the data will be used in our study are time series of
sovereign CDS spread of the countries considered in the sample. These
spreads are used to measure the overall evolution of market returns.
The distributions of the growth of sovereign CDS are calculated
based on the time series of sovereign CDS spreads using the following
formula:
[r.sub.t] = (log ([p.sub.t],)-log ([p.sub.t-1]))* 100 (7)
Due to the complexity of the multivariate GARCH DCC model, our
study is limited to the study of contagion of 10 most dynamic markets in
terms of changes in sovereign CDS spread.
1. Results and interpretations
The following Table 2 shows the estimated parameters of the
multivariate DCC-GARCH model for the quiet period and the crisis period.
After estimating the DCC-GARCH model, we obtain the model
parameters a, P, and co for all countries in the two periods: the quiet
period and the crisis period. Table 2 shows the persistence of
short-term ([alpha]) that remains strong and statistically significant
in most equations of the conditional variance. The parameter a is
generally very close to 0 and much smaller than the parameter [beta]. In
addition, the [beta] coefficient is close to 1 in all countries, except
for the case of Sweden and Germany. This indicates a strong presence of
the phenomenon of long-term persistence. Nevertheless, the sum of the
two parameters ([alpha] + [beta]) is very close to unity. This
demonstrates the importance of the persistence of the conditional
variance of the series studied.
For example, in the case of Greece, the a parameter is four times
smaller than the [beta] parameter. This means that the conditional
volatility of Greece is strongly influenced by the conditional
volatility in the previous period and is less influenced by the new
information. The spread of sovereign CDS depends on the state capacity
to repay its debts to third parties. Therefore, forecasts of future
developments spreads are based on information available today. The
arrival of new market information leads investors to revise the values
of CDS, which vary its spread. This means that the conditional
volatility of spreads is influenced by new information arrival into the
markets.
This is confirmed by the persistence phenomena in the evolution of
correlation between the spread of sovereign CDS. The parameter measuring
the degree of inertia [[theta].sub.2] is close to 1: the more persistent
effects of shocks in the evolution of correlations (i.e., when the
correlation coefficient reaches a given under the effect of shock level,
there is still some time). This coefficient is 0.744. This corroborates
the results on the existence of phenomena marked persistence of
volatility, which is an indicator of the same nature as the covariance
(or correlation). It is not surprising that the phenomenon of
persistence of stylized facts considered in the analysis of variance of
the stock markets, also check for correlations. The [[theta].sub.1]
parameter posted a 0.024 level, considered low, so low weight
significance of recent shocks correlations.
In the following analysis, we focus on the evolution of
correlations adjusted period of stability, and study the projected
future trend. The estimated GARCH DCC (1 .1) allows considering the
spread of the sovereign debt crisis among European countries. The Figure
is available upon request, it illustrate the conditional correlation of
returns of the markets studied, and an overview of the expected 100
observations for the next trend. Since the composition of the sample is
large, the graph is limited by a group of dynamic figure of the
correlation of each country. The correlation coefficients vary over
time: positive and negative changes in all markets. The results of GARCH
DCC (1.1) indicate that during the period 2008-2009, the subprime crisis
has had a clearly significant impact on the conditional correlations
between European countries. We can deduce that the shock affecting
Europe has a significant influence on the spread of sovereign CDS. There
would be compensated (or corrections) the effects of positive and
negative shocks over the long term.
For the crisis period, the parameters of the conditional variance
of the ten markets are relatively close. The persistence of short-term
([alpha]) remains very strong in that quiet period and statistically
significant in most equations of the conditional variance. The positive
[beta] coefficient close to 1 in all cases ranges from 0.623 to 0.92 in
Greece-suede. This indicates a strong presence of the phenomenon of
long-term persistence. The sum of the two parameters ([alpha] + [beta])
is very close to unity. This demonstrates the importance of the
persistence of the conditional variance of the series studied.
For the case of Portugal, the [alpha] parameter is three times
smaller than the [beta] parameter. This means that the conditional
volatility of Portugal is strongly influenced by the conditional
volatility of the previous period, and, is less influenced by the new
information. If these results with that of the quiet period are
compared, we see that the a parameter was 2 times smaller than the
[beta] parameter for the same country. Hence, the effect of the
sovereign debt crisis highlights the influence of the conditional
volatility with the period prior to that period of stability: this means
that the crisis of sovereign CDS spreads are much more influenced by the
new information arrival.
The presence of persistence phenomena in the evolution of
correlation between the spread of sovereign CDS is confirmed. Indeed,
over the parameter measuring the degree of inertia [[theta].sub.2]worth
0.988 here. This corroborates the results on the existence of phenomena
marked persistence of volatility, which is an indicator of the same
nature as the covariance (or correlation). It is not surprising that the
phenomenon of persistence of stylized facts considered in the analysis
of variance of the stock markets, also check for correlations. As a
result of record, [[theta].sub.1] is 0.0087, considered low significance
of the weight of recent shocks on correlations.
In what follows we will be interested in the evolution of
correlations adjusted period of stability, and a study on the projected
future trend and that of 100 observations. The figure is available upon
request, which illustrates the conditional correlation of returns of the
markets studied in crisis and an overview of the expected 100
observations for the next trend. The figure shows that the correlation
coefficients vary over time: positive and negative changes. The results
of GARCH DCC (1.1) react much more similarly to various shocks affecting
the CDS markets in periods of stability. The sovereign debt crisis in
Greece had a clearly significant impact on conditional correlations
between European countries. We can infer that shocks in Europe have a
significant influence on the spread of sovereign CDS. There would be
compensations (or corrections) for the effects of positive and negative
shocks on long period.
C. Impact of Sovereign Debt Crisis in the European Financial System
The sovereign debt crisis in the euro zone began in early 2010 by
the Greek debt crisis. It started with the declaration that the budget
deficit of Greece in 2009 will be more than 12% of its GDP. This is far
from the prescribed figure by the European Union (EU), 3% ceiling. At
this point in time, Greek debt problem triggered. After the downgrade of
its sovereign credit rating, Greece officially begins to suffer from the
crisis of sovereign debt. Three other European countries, namely
Portugal, Ireland and Spain have a deficit level far exceeding the 3%
prescribed in the "Convention on the stability and growth" as
defined by EU.
Despite the financial bailout of the Greek State initiated by other
countries in the euro area and the IMF, rating agencies degrade the
sovereign debt of this country and Ireland's turn to in crisis
following the necessary rescue its banks due to excessive private debt.
The debt of Greece, Spain and Portugal is no longer an issue for
one country, but affects Europe and become a World problem. At the Forum
of Davos 2010 on the global economy, participants indicated that the
next crisis will be that of sovereign debt. Debt problem become a major
concern worldwide. For the debt problem in Europe, it is difficult to
transform short-term sovereign debt crisis, but it will weigh heavily on
the financial market, the forward market approach and economic recovery.
In 2011, Jose Manuel Barroso, President of the European Commission,
announced the possibility of a threat of a "systemic crisis".
Stock markets plunged twice in spring 2010 and summer 2011, the four
international rescue plans (May 2010 and July 2011 for Greece, in
November 2010 for Ireland, in May 2011 for Portugal) have not really
stemmed the spiral of crisis. Financial institutions directly exposed to
sovereign issuers in the euro area have faced a deterioration of both
their access to financing and cost.
When the market value of sovereign debt and bank debt in the euro
zone fell, becoming more volatile, the funding costs increased.
Brokers' levels securities market have been affected because of
their tendency to favor leverage and wholesale funding. Some may have
significant exposure to derivatives on sovereign issuers, which usually
do not require collateral.
To study the spread of sovereign debt crisis in European financial
markets, our study is based on the vector auto-regression model
developed by Johannsen (1991) for several European indices. This model
is one of the most successful, flexible and easy to use templates for
the analysis of multivariate time series. The VAR model has proved
particularly useful for describing the dynamic behavior of economic and
financial time series and forecasting. The model often provides superior
to those of univariate time series forecasts.
This model has several advantages such as the consideration of the
origin of shock, impact its amplitude and duration necessary to
amortization of share. This model is based on modeling of stationary
series. It allows variables to depend on past values of other variables,
and does not limit the dependence only historical and error term.
Consider the following VAR model:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
where Y (t) is a Kxl vector of rates of return in the stock market
column. C is a column vector (Kxl) constant. A(s) is a matrix of
coefficients (KxK). M is the length of delay. And e(t) represents a
vector (lxK.) residues.
E(e(t)) = 0, E(e(t)e' (t - s)) = 0 , [for all]s [not equal to]
0 E(e(t)e'(t))=[alpha] (10)
with [alpha] = {[sigma.sub.ij], i, j, = 1,2,... K.} = positive
matrix size (K * K)
Note that Eun and Shim (1989) requires the determination of the
length of the delay (m-value), or the length is determined through the
use of the following information criteria: Akaike (AIC), Schwartz (SC)
and Hannan-Quinn (HQC). So the value of m is chosen which allows the
minimization of these criteria:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
where [SIGMA]=variance of residuals, K=number of parameters,
T=sample size, and m=length of delay.
This study concerns the transmission of the sovereign debt crisis
in Europe to the financial sector for a sample of countries in the
European Union. The data used to analyze the transmission of the crisis
in Europe consists of time series of two rate indices and new market
indices of the sample countries. The study covers a period of nearly
five years from 01 January 2008 to 31 December 2012, in daily frequency,
i.e., 1,276 observations indices. A selection of two sub-periods is a
quiet period, from 01/01/2008 to 14/01/2010 and a crisis period, from
15/01/2010 to 31/12 / 2012. (This selection is based on the date of the
outbreak of the sovereign debt crisis). These values are taken in basis
points and extracted from the base of Bloomberg, Reuters and European
investor data.
1. Descriptive statistics of variables
A variety of statistical tests performed on the iTraxx Europe and
iTraxx SovX and indices markets of the sample are summarized in the
following Tables 4, 5, 6, and 7.
Most studied index is a left oblique distribution with distribution
platikurtique except, in the case of the index of Spain, represents an
oblique distribution right with platikurtique distribution and the
iTraxx SovX index that represents a forward distribution left with a
leptokurtic distribution for the quiet period (01/01/2008 to
14/01/2010).
The descriptive statistics reveal that during the crisis period
from 15/01/2010 until 31/12/2012, most indices represent a right oblique
distribution with distribution platikurtique, except for the case of the
iTraxx Europe index, iTraxx SovX and Greece represent a left oblique
distribution with platikurtique distribution.
The analysis of correlation between indices for the stable period
shows a strong positive correlation between the sign market indices in
Europe ranging from 0.88 between the market index of Portugal and
Finland to reach 0.9761 between index Finland and France. We observe a
strong correlation between CDS indices SOV iTraxx Europe and iTraxx
0.8291. When comparing CDS indices and market indices, the correlation
is strong but negative. The correlation between the indices in the
crisis period, (15/01/2010 to 31/12/2012), reveals a high average
correlation between positive sign market indices in Europe, but lower
than in stable period, between the same markets. We notice a strong
correlation between CDS indices SOV iTraxx Europe and iTraxx 0.7864.
Another finding in the comparison between CDS indices and market indices
since the correlation is strong but negative sign.
III. STUDY STATIONARITY: DICKEY AND FULLER
A series is said to be stationary if it is finite and constant in
time average, linear connections between the past values, present and
future of this variable, are independent of the time factor and its
variance is finally fixed in time. For this study, we use the stationary
Dickey Fuller Augmented (ADF), which is based on the estimate by OLS the
following three models:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)
The principle of ADF test is primarily to determine the number of
delay p necessary to whiten the residuals. In the second step, it
suffices to apply the sequential strategy Dickey Fuller simpler models.
The results for the two periods are summarized in the following
Tables 8, 9, 10, and 11. In order to perform co-integration tests on the
market indices we start by the stationarity. We use for this, Dickey
Fuller increased (ADF). The results show that the level indices are
non-stationary. In fact, the values of the ADF statistics, level, are
all above their critical values for the quiet period and the crisis
period. However, passing the first difference, all these values are
below the different thresholds of 1%, 5% and 10%. All series have become
stationary after differentiated once. Therefore they are incorporated of
order 1,1(1).
IV. COINTEGRATION TEST BETWEEN THE STUDY VARIABLES
The analysis of cointegration identifies the true relationship
between several variables by searching the existence of a cointegrating
vector and eliminating its effect. However, prior to this test, it is
pertinent to first determine the optimal number of delay. Simply first
we give a number of maximum allowable delay. We will ask p max = 6.
Then, we look for the number of delay p* between 1 and 6 (Dickey Fuller
single) and p max that minimizes both AIC and SC information criteria.
It is here in the presence of a diagnostic discrepancy in the use
of these information criteria. The purpose of the introduction of the
delayed terms is to whiten the residuals, that is to say, to control the
autocorrelation of innovations. We seek the minimum structure that
achieves this goal. It adopts an optimal choice of delay p*=l.
A. Testing Granger Causality
The application of the ADF test of stationarity of the series of
market indices and CDS indices show that all series of order 1 (I (1))
are integrated to a threshold of 5%. So, to analyze the causal
relationships for a number of p equal to 1 during the crisis delays. The
results are presented in Table 13.
Note that of causation as the probability does not exceed the
threshold of significance of 5%. We confirm that there are different
relations between Granger markets studied. Most indices are caused by
the index of Portugal and Belgium, so these values are used to better
predict the market index values. There is a correlation in the sense of
Granger between the values of market indices at 5%. If we consider the
index of Athens Greece, we find that the null hypothesis that
"there is no issue in Granger "is rejected for a number of
lags p = 1 for the majority of the indices, except for the case of
indices: OMX (FINLAND) and FTSE (UK).
But the main finding, the iTraxx index SovX, because the sense of
Granger indices: PSI (Portugal), cac40 (France), FTSE (Italy), Athens
(Greece), dax40 (Germany) and IBEX (Spain).
Changes in the index of sovereign CDS present a very significant
effect on the evolution of the market indices in Europe and especially,
the PUGS countries, Germany and France.
B. Cointegration Test
The cointegration test is the test of Johansen (1991, 1995), which
is based on the number of eigenvectors ordered and the value of the
likelihood ratio (LR) calculating the statistical Johansen following:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
with T is the number of observations. r=0 .... K-l. yi is the
largest eigenvalue. [Q.sub.r] is "trace statistic" and it
tests the following hypotheses:
H0: no cointegrating relationship between the series.
H1 : presence of at least one cointegrating relationship between
the series
It is based on the critical values at the 5% and 1% that we accept
or reject H0. If the LR statistic is greater than the critical data at
the 5% and 1% values, we reject H0 and accept H1 and there is at least
one cointegrating relationship between the series studied.
The results of the tests are generated based on the comparison of
the LR statistic with critical values given in the 5% threshold. While
this statistic is higher than the values, there is at least one
cointegrating relationship between markets; otherwise no cointegrating
relationship exists between these markets. The results of the
cointegration tests are summarized in the following tables:
C. Cointegration Test between Indices in A Quiet Period
Inspection of Table 14 shows that during the quiet period, the
result of cointegration tests between the market indices in Europe is
quite significant. These markets follow a path of evolution close. The
results of cointegration tests show that the overall trends in the
indices of these markets seem to be parallel to the period.
By cons, no cointegration relationship is recorded between the
index of SOV and other market indices in Europe. In other words, these
markets do not respond strongly to financial shocks and are far from
being affected by the contagion effect during adverse developments in
the iTraxx Europe index SOV western (that took place during this
period). These markets resist to any increases or decreases that take
place on other financial markets.
However, the observation in Table 14 shows the presence of
different cointegrating relationships between market indices in Europe.
Indeed, it should be noted that except for Germany, all countries share
at least one cointegrating relationship with other markets. This
multiplicity of cointegrating relationships between the groups in
question is a great explanation in the movement of global markets in the
European Union.
The high mobility of capital, the boosting of financial activities
for monetary creation, the creation of new financial products and the
ease with which the provision of international credits, explain the
multiplicity of cointegrating relationships between these groups.
Inspection of Table 15 shows that during the crisis period of the
study, the results of cointegration tests between the market indices in
Europe are lower than recorded in a quiet period. These markets follow a
path of evolution close. The results of cointegration tests reveal that
the overall trend in the indices of these markets seems to be parallel
to the period.
There has been a change in the results of cointegration
relationship between the index recorded SOV and other market indices in
Europe index of Greece, Belgium, France and Portugal. In other words,
these markets respond more strongly to financial shocks and can be
affected by the contagion effect during adverse developments in the
iTraxx Europe index SOV western that took place during this period.
The observation of Table 15 shows the presence of different
cointegrating relationships between market indices in Europe. And
especially among the PIGS countries (Portugal, Italy, Greece and Spain)
and they share at least one cointegrating relationship between them.
This multiplicity of cointegrating relationships between the groups in
question is a great explanation for the effect of the sovereign debt
crisis that hit first Greece and other countries like Italy, Spain,
Portugal and Ireland.
The great bond between European Union countries, the boosting of
financial activities related to money creation can explain the
multiplicity of cointegrating relationships between these different
groups.
D. The Impulse Response Functions
Following the implementation of the various cointegration tests on
the market indices with SOV iTraxx index, we now come to the heart of
the analysis of VAR models. A model which models inherently dynamic
relationships between a group of selected variables to characterize a
particular economic phenomenon. The pulse analysis will allow
determining the influence of a shock related to the evolution of a
variable on the other variables of the system. We will test the relative
importance of each shock in explaining fluctuations SOV iTraxx index.
The following figures depict the impulse response functions. We
look at the effects of the shock of 10 periods (that is to say 10
years). This horizon represents the time required for the variables back
to their long-run levels.
The graphs describe the impulse responses of the ITraxx index SOV
on different stock market indices in Europe during the crisis of
sovereign debt. When the index occurred in Greece, Belgium and Portugal
shock, generated results are identical. It is clear that the ITraxx
index SOV has no contemporary impact in the first period on these
indexes, since the curve departs the origin. But, soon a negative effect
beginning of the second period before payback in the sixteenth time to
return to its long term.
The case of Germany shows that the impulse response curve departs
the origin and effect positive shock occurred on the index. This effect
disappears seventh period to return to its long-term.
For Finland, the ITraxx index SOV has no impact on the contemporary
OMX 30 index since the impulse response is always zero during the 10
periods. For France and the United Kingdom, we see that the impulse
response curve departs the origin, then the negative effect of shock
came on the index, this effect continued long-term level.
For Italy and Spain, we see that the impulse response curve departs
the origin. Hence, the ITraxx index SOV has no contemporary impact on
these indexes. This effect continues until the sixth period, and a
positive effect of shock came on the index during the sixth and seventh
period, and this effect quickly disappears to return to its long-term
level.
The ITraxx index EUROPE reacts with the amplitude more students
from other indices. In fact soon the first period, a positive impact on
the index results in a positive effect on ITRAXX SOV dice the first
period. This effect disappears in the fifth period. During the seventh
period, there has been a fall reflecting a negative reaction from the
ITraxx index EUROPE.
V. CONCLUSION
We explore the dynamics of the financial sector near the financial
crisis for the sovereign debt crisis in Europe. We focus on the
mechanism that was at the origin of its amplification and highlight the
transmission of shocks to volatility of the sovereign debt crisis in
Europe and in particular in Greece. We check empirically contagion by
analyzing the evolution of sovereign CDS spreads of countries peripheral
Europe, via the DCC GARCH (1.1) multi varied.
Figure 3
We conduct a second empirical verification of the transmission of
shocks to volatility of sovereign debt crisis. We investigate the
financial crisis in Europe and the measurement of the magnitude of these
shocks transmitted through contagion. We use VAR in conducting the
analysis of the results of cointegration tests and impulse functions.
The results emerged from the DCC G ARCH model (1.1) allows us to
find that the conditional correlation of returns react more similarly to
various shocks affecting the CDS markets that recorded in periods of
stability. The sovereign debt crisis in Greece clearly had a significant
impact on the conditional correlations between the countries of Europe.
We can infer that shocks in Europe have a significant influence on the
spread of sovereign CDS. There would be compensations (or corrections)
effects of both signs positive and negative shocks over the long term.
We analyze the Johansen co-integration test for market indices. The
markets respond more strongly to financial shocks and can be affected by
the contagion effect during adverse developments in the ITraxx Europe
index SOV western that took place during this period.
Finally, due to the decomposition of the forecast error variance
that arises from the impulse response function to detect the impact of a
shock on ITRAXXSOV index and its effects on other market indices were
have found that the sensitivity indices opposite the index CDS is not
the same and differs depending on the market in question and that it
depends on the transmission channel especially the degree of dependence
of the relevant market.
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Makram Bellalah (a), Mondher Bellalah (b), Haifa Boussada (c)
(a) Universite de Picardie Jules Verne, France
Makram. bellalah@u-picardie.fr
(b) Universite de Cergy and ISC Paris, France
Mondher. bellalah@u-cergy.fr
(c) Universite Mediterraneenne de Tunis, Tunisia
haifaboussada@gmail. com
Table 1
Correlation matrix of the sovereign CDS spread of the European Union
countries (crisis period)
Germany Austria Belgium Danmark Spain Finland France
Germany 1.00 0.35 0.77 0.72 0.62 0.04 0.94
Austria 0.35 1.00 0.39 0.52 -0.03 0.51 0.26
Belgium 0.77 0.39 1.00 0.83 0.76 -0.25 0.83
Danmark 0.72 0.52 0.83 1.00 0.72 -0.20 0.75
Spain 0.62 -0.03 0.76 0.72 1.00 -0.55 0.73
Finland 0.04 0.51 -0.25 -0.20 -0.55 1.00 -0.15
France 0.94 0.26 0.83 0.75 0.73 -0.15 1.00
Greece 0.68 -0.10 0.77 0.68 0.85 -0.62 0.80
Irland 0.78 0.43 0.71 0.84 0.60 -0.06 0.78
Italy 0.80 -0.00 0.80 0.68 0.87 -0.36 0.89
Portugal 0.84 0.22 0.83 0.80 0.78 -0.33 0.91
UK 0.34 0.19 0.66 0.58 0.71 -0.51 0.45
Sweden 0.85 0.35 0.57 0.52 0.40 0.27 0.81
Greece Irland Italy Portugal UK Sweden
Germany 0.68 0.78 0.80 0.84 0.34 0.85
Austria -0.10 0.43 -0.00 0.22 0.19 0.35
Belgium 0.77 0.71 0.80 0.83 0.66 0.57
Danmark 0.68 0.84 0.68 0.80 0.58 0.52
Spain 0.85 0.60 0.87 0.78 0.71 0.40
Finland -0.62 -0.06 -0.36 -0.33 -0.51 0.27
France 0.80 0.78 0.89 0.91 0.45 0.81
Greece 1.00 0.62 0.87 0.88 0.59 0.44
Irland 0.62 1.00 0.65 0.80 0.27 0.59
Italy 0.87 0.65 1.00 0.86 0.57 0.68
Portugal 0.88 0.80 0.86 1.00 0.51 0.62
UK 0.59 0.27 0.57 0.51 1.00 0.17
Sweden 0.44 0.59 0.68 0.62 0.17 1.00
Statistics provided by authors with Eviews (Version 7.0)
Table 2
Statistics of GARCH (1.1) multi varied (quiet time)
U.K FRANCE Germany Italy Spain
w 3.11 (*) 15.17 (*) 21.59 (*) 0.45 (*) 3.34 (*)
(3.84) (6.12) (9.65) (2.58) (3.67)
X 0.59 (*) 0.51 (*) 1.72 (*) 0.19 (*) 0.30 (*)
(6.94) (4.75) (7.02) (6.85) (4.54)
B 0.58 (*) 0.25 (*) 0.00 (*) 0.83 (*) 0.61 (*)
(16.42) (3.48) (4.46) (55.78) (8.62)
Multivariate
DCC equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[[theta].sub.1] 0.02 (*)
(2.70)
[[theta].sub.2] 0.74 (*)
(6.77)
PORTUGAL SUEDE GREECE BELGIUM IRLAND
1.67 (*) 22.62 (*) 2.25 (*) 0.71 (*) 1.95 (*)
w (4.35) (7.91) (3.77) (3.06) (2.62)
0.30 (*) 0.29 (*) 0.20' 0.17 (*) 0.14 (*)
x (7.02) (3.40) (6.07) (5.92) (4.36)
[beta] 0.72 (*) 0.10 (*) 0.77 (*) 0.81 (*) 0.78 (*)
(28.48) (1.02) (27.10) (29.83) (14.37)
Multivariate DCC equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII]
Statistics provided by authors with WINRATS (Version 8.2)
(*): Statistical significance at the 1% level.
Table 3
Statistics of multivariate GARCH (1.1) (crisis time)
U.K FRANCE Germany Italy Spain
2.82 (*) 0.29 (*) 1.72 (*) 1.63 (*) 0.88 (*)
w (2.80) (1.49) (0.61) (1.32) (0.39)
0.24 (*) 0.09 (*) 0.15 (*) 0.19 (*) 0.14 (*)
x (3.74) (4.37) (1.29) (1.12) (0.85)
[beta] 0.65 (*) 0.90 (*) 0.74 (*) 0.75 (*) 0.83 (*)
(10.95) (43.98) (2.90) (5.13) (3.69)
Multivariate
DCC equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[[theta].sub.1] 0.01 (*)
(5.64)
[[theta].sub.2] 0.98 (*)
(147.49)
PORTUGAL Sweden GREECE Belgium Irish
1.21 (*) 0.20 (*) 1.93 (*) -0.07 (*) 1.05 (*)
w (0.90) (1.65) (0.86) (-0.34) (1.51)
0.15 (*) 0.05 (*) 0.36 (*) -0.01 (*) 0.32 (*)
x (1.70) (2.25) (5.30) (-1.24) (6.56)
[beta] 0.79 (*) 0.94 (*) 0.62 (*) 1.01 (*) 0.68 (*)
(5.29) (36.17) (3.63) (34.23) (9.94)
Multivariate
DCC equation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Statistics provided by authors with WTNRATS (Version 8.2).
(*) significance at the 1% level.
Table 4
Descriptive statistics indices (quiet time)
PS1_20 OMX ITRAXX ITRAX IBEX FTSE
POR FINL EUROPE SOV ESP ITALIE
Mean 8206.95 2012.68 115.53 67.66 10968.31 24481.37
Median 8153.75 1924.40 103.06 56.10 11373.30 22752.00
Max 13026.66 3010.11 216.37 165.98 15101.90 38447.00
Min 5740.17 1189.09 49.63 24.82 6808.10 12639.00
Std Dev. 1712.02 500.92 37.03 29.50 1912.21 6185.08
Skew 0.67 0.35 0.68 1.30 -0.10 0.42
Kurtsosis 2.51 1.80 2.38 3.80 2.01 2.01
JarqueBera 43.82 41.89 48.81 159.55 22.02 36.91
Prob 0.00 0.00 0.00 0.00 0.00 0.00
Obs 521 521 521 521 521 521
FTSE DAX 30 CAC_40 BEL20 ATHE
Roy ALL FRANCE BEL GRECE
Mean 4970.48 5614.00 3851.68 2618.36 2767.31
Median 5088.47 5637.21 3767.22 2469.54 2433.24
Max 6479.40 8045.97 5598.93 4122.82 5207.44
Min 3512.09 3677.07 2520.22 1564.31 1469.41
Std Dev. 738.80 980.55 733.99 731.62 927.60
Skew 0.05 0.12 0.33 0.57 0.68
Kurtsosis 1.80 2.03 1.98 1.94 2.29
JarqueBera 31.49 21.57 32.21 52.63 50.51
Prob 0.00 0.00 0.00 0.00 0.00
Obs 521 521 521 521 521
Statistics provided by Eviews (Version 7.0)
Table 5
Descriptive statistics indices (crisis time)
PSI_20 OMX ITRAXX ITRAX IBEX FTSE
POR FINL EUROPE sov ESP ITALIE
Mean 6501.61 2201.89 126.37 208.98 9167.20 18388.60
Median 6721.49 2177.71 118.25 186.50 9276.00 19126.59
Max 8340.46 2710.77 208.25 383.00 1533.10 23946.44
Min 4393.38 1745.25 72.62 62.00 5950.40 12357.70
Std Dev. 1169.00 242.59 31.91 88.09 1389.37 3152.18
Skew -0.11 0.37 0.57 0.22 -0.31 -0.06
Kurtsosis 1.45 2.18 2.36 1.81 1.96 1.53
JarqueBera 77.16 38.48 53.70 50.16 46.31 68.73
Prob 0.00 0.00 0.00 0.00 0.00 0.00
Obs 753 753 753 753 753 753
FTSE DAX_30 CAC_40 BEL_20 ATHE
Roy ALL FRANCE BEL GRECE
Mean 5629.87 6535.08 3555.99 2411.10 1172.94
Median 5696.70 6515.94 3557.51 2432.30 1212.97
Max 6091.33 7618.62 4160.78 2773.19 2166.77
Min 4805.75 5063.59 2754.82 1918.51 475.89
Std Dev. 283.23 597.24 336.95 208.26 448.22
Skew -0.54 -0.15 -0.18 -0.24 0.24
Kurtsosis 2.31 1.91 1.93 1.96 1.76
JarqueBera 51.44 40.41 40.01 41.12 55.55
Prob 0.00 0.00 0.00 0.00 0.00
Obs 753 753 753 753 753
Statistics provided by Eviews (Version 7.0)
Table 6
Correlation matrix indices (quiet time)
ITraxx Europe ITraxx SovX CAC 40 DAX 30 FTSE 100
ITraxx Europe 1.00 0.83 -0.69 -0.76 -0.76
ITraxx SovX we 0.83 1.00 -0.74 -0.77 -0.73
CAC 40 -0.69 -0.74 1.00 0.98 0.96
DAX 30 -0.76 -0.77 0.98 1.00 0.97
FTSE 100 -0.76 -0.73 0.96 0.97 1.00
IBEX -0.81 -0.80 0.94 0.96 0.97
BEL 20 -0.63 -0.67 0.97 0.95 0.94
FTSE MIB -0.60 -0.71 0.97 0.95 0.91
PSI 20 -0.68 -0.65 0.90 0.89 0.91
OMX HELSINKI -0.64 -0.72 0.98 0.96 0.94
ATHENS -0.60 -0.68 0.94 0.92 0.89
IBEX BEL 20 FTSE MIB PSI 20 OMX 25 ATHE
ITraxx Europe -0.80 -0.63 -0.60 -0.68 -0.64 -0.60
ITraxx SovX we -0.90 -0.67 -0.71 -0.65 -0.72 -0.68
CAC 40 0.94 0.97 0.97 0.90 0.98 0.94
DAX 30 0.96 0.95 0.95 0.89 0.96 0.92
FTSE 100 0.97 0.94 0.91 0.91 0.94 0.89
IBEX 1.00 0.92 0.89 0.92 0.91 0.88
BEL 20 0.92 1.00 0.96 0.94 0.97 0.97
FTSE MIB 0.89 0.97 1.00 0.87 0.99 0.95
PSI 20 0.92 0.94 0.87 1.00 0.88 0.93
OMX HELSINKI 0.91 0.97 0.99 0.88 1.00 0.94
ATHENS 0.88 0.97 0.95 0.93 0.94 1.00
Table 7
Correlation matrix indices (crisis)
ITraxx Europe ITraxx SovX CAC40 DAX30 FTSE 100
ITraxx Europe 1.00 0.79 -0.89 -0.30 -0.32
ITraxx SovX we 0.79 1.00 -0.67 -0.12 0.01
CAC 40 -0.89 -0.67 1.00 0.44 0.51
DAX 30 -0.30 -0.11 0.44 1.00 0.81
FTSE 100 -0.32 0.01 0.51 0.81 1.00
IBEX -0.75 -0.61 0.77 -0.07 0.03
BEL 20 -0.89 -0.75 0.91 0.37 0.36
FTSE MIB -0.86 -0.73 0.88 0.12 0.14
PSI 20 -0.78 -0.67 0.80 -0.03 0.03
OMX HELSINKI -0.60 -0.45 0.66 0.34 0.43
ATHENS -0.84 -0.80 0.78 -0.11 -0.08
IBEX BEL 20FTSE MIB PSI 20 OMX 25 ATHE
ITraxx Europe -0.75 -0.89 -0.86 -0.78 -0.61 -0.84
ITraxx SovX we -0.61 -0.75 -0.73 -0.67 -0.45 -0.80
CAC 40 0.77 0.91 0.88 0.80 0.66 0.78
DAX 30 -0.07 0.37 0.12 -0.03 0.34 -0.11
FTSE 100 0.03 0.36 0.14 0.03 0.43 -0.08
IBEX 1.00 0.75 0.89 0.94 0.64 0.90
BEL 20 0.75 1.00 0.85 0.81 0.68 0.79
FTSE MIB 0.89 0.85 1.00 0.92 0.58 0.92
PSI 20 0.94 0.81 0.92 1.00 0.65 0.93
OMX HELSINKI 0.64 0.68 0.58 0.65 1.00 0.52
0.90 0.79 0.92 0.93 0.52 1.00
Table 8
ADF test level (quiet time)
Variables t statistic Value Value
critique 1% critique 5%
GREECE -2.75 -3.44 -2.87
Belgium -2.13 -3.44 -2.87
France -2.33 -3.44 -2.87
Germany -2.45 -3.44 -2.87
UK -2.03 -3.44 -2.87
Italy -2.25 -3.44 -2.87
Spain -2.19 -3.44 -2.87
itraxx sov -1.95 -3.44 -2.87
itraxx Europe -1.92 -3.44 -2.87
Finland -1.97 -3.44 -2.87
Portugal -2.97 -3.44 -2.S7
Variables Value Stationarity
critique 10%
GREECE -2.57 No
Belgium -2.57 No
France -2.57 No
Germany -2.57 No
UK -2.57 No
Italy -2.57 No
Spain -2.57 No
itraxx sov -2.57 No
itraxx Europe -2.57 No
Finland -2.57 No
Portugal -2.57 No
Table 9
ADF test level(crisis time)
Variables t statistic Value Value
critique 1% critique 5%
GREECE -1.51 -3.44 -2.87
Belgium -2.23 -3.44 -2.87
France -2.39 -3.44 -2.87
Germany -1.81 -3.44 -2.87
UK -2.97 -3.44 -2.87
Italy -1.92 -3.44 -2.87
Spain -1.95 -3.44 -2.87
itraxx sov -1.62 -3.44 -2.87
itraxx Europe -2.28 -3.44 -2.87
Finland -1.93 -3.44 -2.87
Portugal -1.16 -3.44 -2.87
Variables Value Stationarity
critique 10%
GREECE -2.57 No
Belgium -2.57 No
France -2.57 No
Germany -2.57 No
UK -2.57 No
Italy -2.57 No
Spain -2.57 No
itraxx sov -2.57 No
itraxx Europe -2.57 No
Finland -2.57 No
Portugal -2.57 No
Table 10
ADF test in first difference (quiet time)
Variables t statistic Value Value
critique 1% critique 5%
GRECE -21.55 -3.44 -2.87
Belgique -26.83 -3.44 -2.87
France -27.63 -3.44 -2.87
Allemagne -23.19 -3.44 -2.87
Royaume-Uni -24.96 -3.44 -2.87
Italie -26.54 -3.44 -2.87
Espagne -25.74 -3.44 -2.87
itraxx sov -17.86 -3.44 -2.87
itraxx Europe -16.83 -3.44 -2.87
Finland -23.33 -3.44 -2.87
Portugal -24.48 -3.44 -2.87
Variables Value Stationarity
critique 10%
GRECE -2.57 No
Belgique -2.57 No
France -2.57 No
Allemagne -2.57 No
Royaume-Uni -2.57 No
Italie -2.57 No
Espagne -2.57 No
itraxx sov -2.57 No
itraxx Europe -2.57 No
Finland -2.57 No
Portugal -2.57 No
Table 11
ADF test in first difference (crisis time)
Variables t statistic Value Value
critique 1% critique 5%
GREECE -25.89 -3.44 -2.87
Belgium -29.74 -3.44 -2.87
France -27.85 -3.44 -2.87
Germany -27.56 -3.44 -2.87
UK -26.83 -3.44 -2.87
Italy -28.27 -3.44 -2.87
Spain -29.85 -3.44 -2.87
itraxx sov -25.35 -3.44 -2.87
itraxx Europe -26.01 -3.44 -2.87
Finland -26.43 -3.44 -2.87
Portugal -28.48 -3.44 -2.87
Variables Value Stationarity
critique 10%
GREECE -2.57 No
Belgium -2.57 No
France -2.57 No
Germany -2.57 No
UK -2.57 No
Italy -2.57 No
Spain -2.57 No
itraxx sov -2.57 No
itraxx Europe -2.57 No
Finland -2.57 No
Portugal -2.57 No
Table 12
Choice of the optimal number of delay
VARI VAR2 VAR3 VAR4 VAR5 VAR6
AIC 117.98 117.79 117.60 117.35 117.27 117.20
SC 118.52 118.81 119.12 119.36 119.77 120.19
The Akaike criterion (AIC) leads to a delay optimal choice p* =5, while
the Schwartz criterion (SC) leads to p*=1.
Table 13
Granger causality relationship between the indices in crisis
Granger PSI_20 POR OMX FINAL ITRAXX EUROPE SOVX EUROPE
causality test
PSI_20 + + -
PORTUGAL
OMX + + -
FINLAND
ITRAXX - + +
EUROPE
ITRAX_SOV + - +
EUROPE
IBEX Spain + + + +
FTSE ITALy + + - -
FTSE UK + + + -
DAX30 + + - +
Germany
CAC_40 + + + +
FRANCE
BEL_20 + + + +
BELGIQUE
ATHENS
GREECE + - + +
Granger IBEX ESP FTSE ITAL FTSE UK DAX_30 ALLE
causality test
PSI_20 + + - -
PORTUGAL
OMX - + - +
FINLAND
ITRAXX - + - +
EUROPE
ITRAX_SOV + + - +
EUROPE
IBEX Spain + + -
FTSE ITALy - - +
FTSE UK - + +
DAX30 + + -
Germany
CAC_40 + + - +
FRANCE
BEL_20 - + + -
BELGIQUE
ATHENS
GREECE + + - +
Granger CAC_40 FRANCE BEL 20 BELG ATHENS GREECE
causality test
PSI_20 + + +
PORTUGAL
OMX + + +
FINLAND
ITRAXX + + -
EUROPE
ITRAX_SOV + - +
EUROPE
IBEX Spain + + -
FTSE ITALy + - -
FTSE UK + - +
DAX30 + - +
Germany
CAC_40 + +
FRANCE
BEL_20 + -
BELGIQUE
ATHENS
GREECE + +
Statistics provided by Eviews (Version 7.0)
The "+" indicates the existence of a significant causal relationship
between the variable and the column line.
The "-" means that the column variable does not Granger cause under the
variable line.
Table 14
Cointegration test between the indices in quit time:
Johansen test PSI_20 POR OMX FIN ITRAXX EUR sovx EUR IBEX ESP
PSI_20 2 0 2 2
PORTUGAL
OMX 0 0 1
FINLAND
ITRAXX 2 0
EUROPE
ITRAX_SOV 0
EUROPE
IBEX Spain
FTSE ITALIy
FTSE UK
DAX_30
Germany
CAC_40
FRANCE
BEL_20
BELGIUM
ATHENS
GREECE
Johansen test FTSE ITAL FTSE UK DAX_3 GERMAN CAC_40 FRAN
PSI_20 2 2 2 2
PORTUGAL
OMX 1 1 2 2
FINLAND
ITRAXX 2 0 0 0
EUROPE
ITRAX_SOV 0 0 0 0
EUROPE
IBEX Spain 2 2 2 2
FTSE ITALIy 1 2 2
FTSE UK 1 1
DAX_30 2
Germany
CAC_40
FRANCE
BEL_20
BELGIUM
ATHENS
GREECE
Johansen test BEL_20 BEL ATHENS GREECE
PSI_20 2 2
PORTUGAL
OMX 2 2
FINLAND
ITRAXX 0 0
EUROPE
ITRAX_SOV 0 0
EUROPE
IBEX Spain 0 0
FTSE ITALIy 1 2
FTSE UK 2 0
DAX_30 1 2
Germany
CAC_40 1 2
FRANCE
BEL_20 2
BELGIUM
ATHENS
GREECE
Table 15
Cointegration test between the indices in times of crisis:
Johansen test PSI20 POR OMX FINL ITRAXX EUR SOVX EUR IBEX ESP
PSI_20
PORTUGAL
OMX 0
FINLAND
ITRAXX 1 2
EUROPE 1
ITRAX SOV 1 0 1
EUROPE
IBEX SPAIN 1 0 1 0
FTSE_MIB 1 1 1 0 1
ITALY
FTSE100 UK 0 2 2 0 2
DAX_30 0 0 0 0 0
GERMANY
CAC_40 1 2 2 2 0
FRANCE
BEL_20 1 1 1 1 1
BELGIUM
ATHENS 1 0 1 1 1
GREECE
Johansen test FTSE ITAL FTSE UK DAX30 GERMA CAC40 FRAN BEL20 BEL
PSI_20
PORTUGAL
OMX
FINLAND
ITRAXX
EUROPE
ITRAX SOV
EUROPE
IBEX SPAIN
FTSE_MIB
ITALY
FTSE100 UK 2
DAX_30 0 2
GERMANY
CAC_40 1 0 2
FRANCE
BEL_20 1 2 0 1
BELGIUM
ATHENS 1 0 0 0 1
GREECE
Johansen test ATHENS GREECE
PSI_20
PORTUGAL
OMX
FINLAND
ITRAXX
EUROPE
ITRAX SOV
EUROPE
IBEX SPAIN
FTSE_MIB
ITALY
FTSE100 UK
DAX_30
GERMANY
CAC_40
FRANCE
BEL_20
BELGIUM
ATHENS
GREECE
