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DYNAMIC ECONOMETRIC MODELS 
Vol. 11 – Nicolaus Copernicus University – Toruń – 2011 

Agata Kliber  
Poznan University of Economics 

Sovereign CDS Instruments in Central Europe –  
Linkages and Interdependence†  

A b s t r a c t. In the article, linkages among sovereign CDS instruments in Central Europe are 
investigated. Special attention is paid to the change of causality patterns during the Hungarian and 
Greek crises. The results of the research reveal that the expectations do play a role in determining 
the prices of the contracts, as well as that there exist regional causality relationships between the  
instruments. The strength of causality between the volatilities of Polish – Hungarian and Czech-
Hungarian CDS prices weakened during the Hungarian crisis, while the volatilities of the three 
time series reacted rapidly and strongly to the Greek one. This suggest that the European events 
should play more important role in determining the dynamics of the contracts than the problems 
of the country of the weakest fundamentals in the region. 

K e y w o r d s: multivariate volatility, credit default swap, contagion, sunspot, Central Europe.  

Introduction   

 Sovereign CDS contracts attracted special attention of the researchers start-
ing from the outbreak of the recent financial crisis. Beforehand, most of the 
research concentrated on the corporate CDS contracts and analysed interrela-
tions of the CDS spreads with other financial instruments. To name a few: Hull, 
Predescu and White (2004) analysed relationships between the CDS spreads, 
bond yields and credit rating announcements over the period 1998-2002. 
Benkert (2004) searched for the factors explaining the dynamics of the CDS 
premia, finding option-implied volatility especially significant in explaining 
their variability. Some studies concentrated on the interrelations between the 
premia of the corporate CDS contracts. Such an example can be the paper by 
Coudert and Gex (2008) in which the authors analyse possible contagion of the 

                                                 
† The work is supported by the Polish Ministry of Science and Higher Education through the 

Project NN 112372340. The author would like to thank the members of the project, especially 
Jacek Wallusch and Michał Adam for their help, cooperation and fruitful comments on the article, 
as well as the two anonymous referees for their useful and inspiring remarks. 



Agata Kliber 112 

crisis experienced by General Motors and Ford in May 2005 to the whole CDS 
market. Jorion and Zhang (2007) show how information of credit event of 
a given company is transferred among the other companies through the CDS 
market in USA over the period 2001–2004.  

 Most recently, more and more attention is paid to the interrelations between 
the sovereign CDS instruments. An example can be the work of Calice, Chen 
and Williams (2011) in which the authors analyse the interrelations between the 
CDS contract and bonds markets in the Eurozone. Alter and Schüler (2011) 
investigated interdependence of the sovereign and banks’ CDS series of chosen 
European countries (France, Germany, Italy, Ireland, Netherlands, Portugal and 
Spain). Alfonso, Furceri and Gomes (2011) carried an event-study analysis to 
check the reaction of sovereign bond yields and CDS spreads to the rating agen-
cy announcements, finding among all that the reaction of the CDS spreads to 
the negative news increased after the Lehman Brothers’ bankruptcy. The dataset 
used by the authors included EMU and non-EMU countries, among all Czech 
Republic, Hungary and Poland, and covers the period from January 1995 to 
October 2010.  

 The aim of this paper is to investigate possible linkages and interdepend-
ence among Central European sovereign CDS instruments of 5 year maturity 
during the hectic period of recent financial crisis. The author wants to verify 
whether the price of the sovereign CDS instruments is determined mainly by 
fundamentals or whether the premium is influenced by expectations (sunspots). 
The author first analyses volatilities of the CDS spreads to find any common 
patterns of their dynamics. Next, the non-causality test of Cheung and Ng 
(1996) is run to verify the possible moments of causality and to relate them to 
the crisis events. Eventually, to check the strength of causality, the author esti-
mates the multivariate stochastic volatility model with Granger-causality of Yu 
and Meyer (2006). The results of the research show that the price of the instru-
ments is indeed influenced by expectations (e.g. a significant reaction of volatil-
ities to the Greek crisis was found). Regional linkages (measured by Granger-
causality relations) do exist, but in the analysed period they played less im-
portant role (reaction of volatilities of Polish and Czech instruments to the Hun-
garian problems was not comparable to their reaction to the Greek crisis). The 
finding that the negative events influence significantly the price of the CDS is 
consistent with the previous finding, cited above.  

1.  CDS Instruments – an Overview 

 Credit Default Swap (in short: CDS) is an instrument that gives the holder 
right to sell a bond for its face value in the event of a default by the issuer (Hull, 
2008). This credit derivative constitutes a form of insurance which protects the 
buyer of the CDS in the case of a loan default by particular company.  
The company is known as the reference entity and a default by the company is 



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 113

known as a credit event. The buyer of the CDS makes periodic payments to the 
seller until the end of life of the CDS or until a credit event occurs. The total 
amount paid per year as a percent of the notional principal to buy the protection 
is called the CDS spread (Hull, 2008).  

 Many different companies and countries are reference entities for the CDS 
contracts. Special kinds of CDS contracts are the sovereign ones, the underlying 
instruments of which are government bonds. Spreads of such CDS instruments 
can be also used as indicators of the credit-worthiness of a given country (Hull, 
2008). Usually, each negative (and positive) piece of information about finan-
cial situation of a given country is reflected in the CDS spread. It is noticeable 
that negative information contributes to the growth of the CDS premia, while 
the positive one – to its lowering. The more liquid the market, the more percep-
tible are these movements. The sovereign debt market has attracted considerable 
attention since September 2008, while before the crisis trading concentrated on 
private sector instruments (Fontana, Scheicher, 2010). 

2.  CDS Instruments in Central Europe 

 Let us take a look at the Figure 1. It presents the dynamics of the CDS 
spreads of 5 year maturity quoted for Czech Republic, Hungary and Poland over 
the period March 2008 – March 2011. First of all, we can notice that the spreads 
for Hungary are the highest. Next, we can observe some similarities in the be-
haviour of all the three spreads. There was a significant jump in the middle of 
October 2008.  

 According to the Financial Stability Report (NBP, 2009) “the rise in CDS 
premium on the Polish government debt was largely connected with the global 
tendency to assess credit risk very prudently and the negative impact of the 
situation in the region on perception of investment risk in Poland”. Moreover, 
the probability of default of the Polish government implied by the prices of 
CDS was much higher than other ratings suggested. The rating implied by the 
CDS prices was BBB, while Moody’s assessment was A2 and S&P’s and 
Fitch’s: A-. On contrary, the rating for Hungary was lowered several times in 
2008 and 2009. For example, on October 15th the rating for Hungary was 
changed by S&P from A2 to A2 with negative outlook.  The rating was lowered 
again on November 17th, 2008 and on March 30th, 2009.  The changes in ratings 
appeared rather seldom and were not as sharp as the dynamics of the CDS pric-
es could suggest.  

  In the second half of 2009 the situation stabilised. Since the beginning of 
2010 the CDS premia in the three countries decreased, falling to the lowest lev-
els since September 2008. However, in May 2010 the rise in risk aversion con-
nected with Greek insolvency affected also the Central European CDS market. 
Thus, we could observe the rise in the CDS premia to the level recorded in the 
second quarter of 2009. On May 9th, the European Stabilisation Mechanism has 



Agata Kliber 114 

been announced and shortly afterwards the risk assessment of Central European 
Bonds improved (NBP, 2010). However, in June it rose again. The highest 
growth was observed in Hungary. This growth of the CDS premium in Hungary 
can be also explained by the worsening economic situation of the country. Al-
ready on June 3rd, a leader of the ruling Fidesz party said that the country's fi-
nances were in much worse condition than previously expected. Also the vice 
chairman of Fidesz party stated that there was only a slim chance to avoid 
Greek scenario (according to: www.napi.hu). In consequence, the five-year 
Credit Default Swaps on Hungary rose by 58 basis points to 320 basis points, 
which is reflected in Figure 1. On June 12th, Moody changed its rating for Hun-
gary from BAA1 to BAA3 with negative outlook. Again, on July  17th the EU 
and IMF suspended a review of Hungary’s funding program (which had been 
set up in 2008 to save the country from financial problems) and said that the 
country must have taken action to meet targets for cutting its budget deficits. 
The suspension meant that Hungary would not have access to the remaining 
funds in its loan package. This event could have contributed to the increase of 
the CDS price in the second half of July. Eventually, the pick of the CDS price 
in November can be explained by the reforms of the pension system announced 
by the Hungarian government.  

 
Figure 1. Corporate 5-year CDS spreads in bps for Czech Republic, Poland and Hun-

gary  

2.1. Data Description 

 As already said, the analysed sample covered the period from March 2008 
to March 2011 and consisted of 796 observations. The data was provided by 
Bloomberg. Obviously, the spreads were not stationary, so we run all our tests 
on the changes of the prices ( t t tP P ). We did not take the logarithms of the 
increments to avoid problems with interpretation of such transformed series (the 
prices of the CDS contracts are expressed in basis points). 



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 115

Table 1 presents the descriptive statistics of the increments of the daily changes 
of the prices for Czech Republic, Hungary and Poland. As expected, the highest 
deviation is observed in case of the Hungarian instruments, while the lowest – 
in case of the Czech ones. 

Table 1.  Descriptive statistics of the price changes of the Central European CDS 

Variable Min Value Mean Value Max Value Std. Deviation 
dCDS_CZ -57.503 0.038 54.998 6.693 
dCDS_HU -83.332 0.156 98.033 14.294 
dCDS_PL -46.654 0.064 47.333 8.154 

date 10.03.2008     - 28.03.2011 - 

3.  Non-causality Analysis – Tests Based upon the GARCH-type 
Models 

 In order to test whether expectations play a role in CDS pricing, we tested 
for the volatility interactions in the CDS prices. Detecting volatility spillovers in 
the data is the sign of contagion. The type of contagion which is expectation-
driven is called sunspot – see e.g. (Keister, 2006). The occurrence of the sun-
spot is connected with the period of volatility growth – thus we first estimate 
univariate volatility models to test for possible moments of contagion.  

3.1. Volatility Dynamics of the CDS Prices – a Univariate GARCH  
Analysis 

 To begin with, we first fit univariate GARCH models to the data and 
searched for the moments of higher volatility. As stated before, the moments of 
abnormal volatility growth can indicate the sunspot event. Thus, we fit the 
GARCH models to each of the series. Since in each case the sum of the parame-
ters  and    in estimated GARCH(1,1) models exceeded 1, we decided for 
IGARCH models with Student distribution. In case of Hungarian and Polish 
CDS it was also necessary to account for ARMA effect in the conditional mean 
equation, as well as to assume Student distribution. Each of the fitted model was 
successfully tested against autocorrelation in mean (Box-Pierce test) as well as 
ARCH effect (Engle test) and stability of the parameters (Nyblom test).  
All computations presented in this paragraph were performed using OxMetrics 
6 with package G@RCH. Tables 2– 4 present the estimated parameters, while 
the Figures 2 to 4 the estimates of volatilities of each time series. 

Table 2.  Estimates of ARMA(0,0)-IGARCH model for Czech CDS  

Coefficient Estimated value Std. Error p-value 
 0.248   0.181 - 
 0.175 0.043 0.000 
 0.825 - - 

Note: All parameters appeared to be stable, according to the Nyblom stability test.  



Agata Kliber 116 

Table 3.  Estimates of ARMA(1,0)-IGARCH(1,1) model for Polish CDS 

Coefficient Estimated value Std. Error p-value 
AR(1) 0.136 0.040 0.001 
 0.344 0.195 - 
 0.188 0.029 0.000 
 0.812 - - 

Degrees of freedom 4.867     0.632 - 
Note: All parameters appeared to be stable, according to the Nyblom stability test. 

Table 4.  Estimates of ARMA(0,1)-IGARCH(1,1) model for Hungarian CDS 

Coefficient Estimated value Std. Error p-value 
MA(1) 0.163 0.036 0.000 
 3.616 1.937 - 
 0.280 0.088 0.002 
 0.720 - - 

Degrees of freedom 3.881 0.460 - 
Note: All parameters appeared to be stable, according to the Nyblom stability test. 

 We plot the obtained estimates of conditional variances in Figures 2–4. We 
can observe that the moments of volatility growth in the three countries overlap. 
The first one started in September 2008 and was most probably connected with 
the worldwide financial crisis. The second one started in May 2010 and may 
have two causes. Either it was the reaction for the Greek crisis or the echo of the 
turmoil in Hungary. It is worth noting that the second pick of volatility was 
much smaller in the case of Czech CDS price than the one observed for Polish 
and Hungarian CDS price. What is important, during the “second turmoil” we 
observe the picks in volatility on May 11th in the case of the three time series. 
However, in the case of Hungary, this pick is relatively small as compared to 
the one observed on June 7th, which may have been caused by the statements of 
the leaders of the ruling Fidesz party about the very poor economic situation of 
the country. The third pick appeared on July 21st and was most probably the 
consequence of the suspension of the funding program for Hungary. 

 
Figure 2.  Estimates of conditional variance for Czech CDS  



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 117

 
Figure 3.  Estimates of conditional variance for Polish CDS 

 
Figure 4.  Estimates of conditional variance of Hungarian CDS 

3.2. Non-causality Test of Cheung and Ng 

 Based upon the obtained estimates of the volatility of the CDS contracts, we 
computed the statistics of the non-causality test of Cheung and Ng (1996) – see 
the Appendix for details. The statistics are used to test the null hypothesis of no 
causality in variance. Table 5 presents the results. In all the cases the null of no 
causality was rejected. However, the highest value took the statistics obtained 
for Hungarian and Polish CDS variances.  

Table 5.  Statistics of the non-causality in variance test of Cheung and Ng 

j=0,k= CZ→PL PL→CZ HU→PL PL→HU HU→CZ CZ-→HU 2 

1 43.045 43.554 60.905 60.768 23.392 23.392 5.991 

2 43.563 44.105 61.311 61.116 23.410 23.495 7.815 

3 44.436 44.328 61.312 61.119 23.644 24.153 9.488 



Agata Kliber 118 

 Additionally, taking advantage of the statistics constructed for small sam-
ples, we computed the test for the moving window of 120 observations. Let us 
assume that the relationship implied by the test is valid for the period of 120 
days, ending on the day of the window end. We present the results in Figures  
5–10. The points of the second coordinate equal to 1 denote the moments in 
which we rejected the hypothesis of non-causality at lag 1. The pictures reveal 
some interesting patterns. The causality relationships are bilateral (there occurs 
the “feedback” according to the Cheung and Ng terminology). Yet, in the case 
of Poland and Czech Republic, the period of constant causality in variance be-
gins in summer 2009, while in the case of Poland and Hungary – it ends in 
summer 2010. This means that there was a year period of feedback Poland-
Hungary, Poland-Czech Republic, which ended in case of the Poland-Hungary 
relationships in the moment of the turbulence in Hungary. What is interesting, 
the Hungarian crisis did not affect to such extend the causality patterns with 
Czech Republic. Although there appear moments of non-causality, as for exam-
ple in November 2010, in general the null is rejected. However, the fact that in 
November 2010 the causality linkages weakened suggests that the pension crisis 
in Hungary did not affect the way the market participants value the risk of in-
vestment in Czech Republic.  

 
Figure 5.  Periods of causality in variance: Poland - Czech Republic 

 
Figure 6.  Periods of causality in variance: Czech Republic - Poland 

 
Figure 7.  Periods of causality in variance: Czech Republic – Hungary 



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 119

 
Figure 8.  Periods of causality in variance: Hungary - Czech Republic 

 
Figure 9.  Periods of causality in variance: Poland - Hungary 

 
Figure 10.  Periods of causality in variance: Hungary-Poland 

 The results of the test suggest that the two moments of turbulence denoted 
by volatility growth were of different nature. While in the first phase of the 
crisis we could observe significant interrelations between volatility of Polish 
and Hungarian CDS instruments, as well as between Czech and Hungarian 
ones, suggesting that the crisis may have been regional or that at least it was 
considered so by the investors, the situation changed during the second volatili-
ty pick. Although in spring 2010 the null of non-causality was rejected, in 
summer and autumn – when the crisis in Hungary intensified – the causality 
relations weakened significantly. This can suggest that the contagion did occur, 
but its source was outside the Central Europe. Most probably, as suggested in 
the NBP’s  Financial Stability Reports, there was a global growth of risk per-
ception as a reaction to the Greek problems. However, the Hungarian crisis did 
not infect the rest of the analysed Central European countries. It seems that ei-
ther the investors did not perceive the Hungarian problems as contagious or that 
the CDS prices did not reflect the market reality. The latter problem could occur 
if the market was not liquid. However, as presented in Figure 11 the instruments 
are indeed traded intensively, and the most liquid ones are the Hungarian CDS 
contracts. 



Agata Kliber 120 

 

 
Figure 11.  Turnovers on the CDS market - quarterly data 

4. Analysis of Granger Causality in Variance – a Multivariate  
Stochastic Volatility Model 

 The test of Cheung and Ng allows us to test the direction of causality, not 
the strength of it. Thus, we also estimated a model of Yu and Meyer (2006) – 
a Multivariate Stochastic Volatility model with Granger causality (see the Ap-
pendix for details), allowing not only for detecting the causality patterns (in 
Granger sense), but also the strength of them. 

 First, we estimated a VAR equation for the Polish and Hungarian CDS pric-
es in order to account for any linear dependencies in the data. The results are 
presented in Tables 6–7.  Order of equation was chosen using Schwarz infor-
mation criterion. In case of the Hungarian CDS price, it appears that it was in-
fluenced by the past values of this instrument price (lagged value of Polish CDS 
price is insignificant). Similarly, the price of Polish CDS is also influenced by 
the past value of Hungarian CDS price.  

Table 6.  VAR equation for Hungarian CDS (Polish and Hungarian CDS in the system) 

Parameter name Estimate Std. Error P-value 
CDShu(-1) 0.261       0.054         0 
CDSpl(-1) -0.014      0.094        0.878   

Const. 0.079       0.482        0.870    

Table 7.  VAR equation for Polish CDS (Polish and Hungarian CDS in the system) 

Parameter name Estimate Std. Error P-value 
CDSpl(-1) -0.0230     0.054        0.864    
CDShu(-1) 0.154       0.031        0    

Const. 0.047      0.276         0.864    

 The volatility  model was estimated for the residuals from the VAR system, 
using the free software WinBUGS (version 1.4).  Since the program uses the 



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 121

Bayesian approach to the estimation, we assume that all the parameters are sto-
chastic variables. To give the readers an approximation of the point estimates, 
we present the means and medians of the distributions, as well as the standard 
deviations. The results are presented in Table 8. Moreover, in the case of the 
parameters 12 and 21 , we present the obtained density functions (Figure 11 
and 12).  

Table 8.  Results of the estimation of GC-MSV model for Hungarian (1) and Polish (2) 
CDS prices 

Variable name Mean Standard deviation MC error 2.5% percentile Median 97.5% percentile 

1  4.063 0.368 0.025 3.340 4.038 4.858 

2  3.100 0.395 0.027 2.332 3.077 3.964 

1  0.697 0.061 0.004 0.566 0.702 0.803 

2  0.877 0.043 0.003 0.785 0.879 0.954 

12  0.098 0.044 0.003 0.021 0.096 0.192 

21  0.247 0.058 0.004 0.146 0.241 0.373 

1  0.674 0.061 0.004 0.554 0.674 0.796 

2  0.431 0.053 0.005 0.330 0.429 0.537 

  0.752 0.019 0.001 0.714 0.753 0.789 

 Thus, we conclude that there exist causality between the volatility of Polish 
and Hungarian CDS contracts. Based upon the obtained distribution we can 
conclude that the volatility of Polish CDS Granger-causes the volatility of Hun-
garian CDS. Since the result was obtained for the whole sample, we can expect 
that the direction of causality is constant over time.  

Table  9.  VAR equation for Polish CDS (Polish and Czech CDS in the system) 

Parameter name Estimate Std. Error P-value 
Const. 0.054    0.278          0.847    

CDSpl(-1) 0.044       0.047         0.356    
CDSpl(-2) -0.050       0.048        0.296    
CDScz(-1) 0.241        0.057         0 
CDScz(-2) 0.064    0.056         0.259    

Table 10. VAR equation for Czech CDS (Polish and Czech CDS in the system) 

Parameter name Estimate Std. Error P-value 
Const. 0.023       0.227         0.919    

CDSpl(-1) 0.314        0.039         0 
CDSpl(-2) 0.106      0.039        0.006     
CDScz(-1) -0.147      0.047     0.002     
CDScz(-2) -0.184        0.046      0 

 



Agata Kliber 122 

 We followed the same procedure in order to verify the interactions between 
Polish and Czech, as well as Czech and Hungarian CDS prices. The results are 
presented in Tables 9–11. 

  
Figure 12. Density of the parameter 12  

(causality from Poland to Hungary) 
Figure 13. Density of the parameter 21 

(causality from Hungary to Poland) 
 

  

Figure 14. Density of the parameter 21 

(causality from Poland to Czech Re-
public) 

Figure 15. Density of the parameter 12 
(causality from Czech Republic to 
Poland) 

 In case of the interactions between Polish and Czech CDS prices we observe 
that Polish CDS price are influenced by the prices of Czech CDS from the pre-
vious day, while the prices of Czech CDS are influenced by the prices of both 
Polish and Hungarian CDS from one and two days before. In case of the second 
moment dependency, it is again Polish CDS volatility that influences the vola-
tility of the Czech CDS (parameter 21 ). The second “causality parameter” – 

12  – takes smaller value and  its standard deviation amounts to 60% of its 
mean value. Thus, we conclude that the investors do not assess the risk of in-
vestment in Poland based upon the worsening situation of other Central Europe-



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 123

an countries, as before. Moreover, it is the volatility of Polish CDS that affects 
the volatility of the other Central European ones the most. Figures 14 and 15 
present the obtained densities of the causality parameters.  Eventually, we in-
vestigated the causality patterns in case of Hungarian and Czech CDS prices. 
The results are displayed in Tables 12–14. 

Figure 16. Density of the parameter 21 
(causality from Czech Republic to 
Hungary) 

Figure 17. Density of the parameter 12 
(causality from Hungary to Czech Re-
public) 

Table 11.  Results of the estimation of GC-MSV model for Polish (1) and Czech (2)  
CDS prices 

Variable name Mean Standard deviation MC error 2.5% percentile Median 97.5% percentile 

1  3.150 0.365 0.027 2.474 3.150 3.942 

2  2.196 0.421 0.031 1.419 2.190 3.097 

1  0.844 0.080 0.006 0.666 0.856 0.969 

2  0.558 0.125 0.010 0.283 0.562 0.767 

12  0.106 0.065 0.005 0.003 0.096 0.250 

21  0.499 0.151 0.012 0.251 0.493 0.828 

1  0.422 0.073 0.006 0.307 0.412 0.590 

2  0.574 0.095 0.007 0.388 0.572 0.766 

  0.622 0.026 0.001 0.568 0.622 0.669 

 Based upon the estimated VAR model we can conclude that the price of 
Czech CDS depended on the past values of itself and Hungarian CDS price. In 
case of the causality in the second moments, we observe small values of the 
“causality coefficients”. Although the value of 12 is more than two times higher 

than the one of 21 , in both cases the standard deviation of the obtained coeffi-
cients exceed 35% of their means. Thus, we can expect bivariate causality on 



Agata Kliber 124 

quite low level, a little higher in case of Hungarian influence on the volatility of 
Czech CDS. The results are presented in Figure 16 and 17. 

Table 12.  VAR equation for Czech CDS (Czech and Hungarian CDS in the system) 

Parameter name Estimate Std. Error P-value 
Const. 0.025     0.228          0.914    

CDScz(-1) -0.095       0.043        0.027     
CDShu(-1) 0.161        0.021        0 

Table 13. VAR equation for Hungarian CDS (Czech and Hungarian CDS in the system) 

Parameter name Estimate Std. Error P-value 
Const. 0.078       0.481      0.871   

CDScz(-1) 0.143        0.091        0.114    
CDShu(-1) 0.213        0.043        0 

Table 14. Results of the estimation of GC-MSV model for Czech (1) and Hungarian (2) 
CDS prices 

Variable name Mean Standard deviation MC error 2.5% percentile Median 97.5% percentile 

1  2.053 0.394 0.026 1.284 2.051 2.878 

2  4.040 0.334 0.022 3.373 4.035 4.706 

1  0.700 0.091 0.008 0.501 0.714 0.839 

2  0.772 0.068 0.006 0.621 0.777 0.897 

12  0.312 0.109 0.010 0.153 0.293 0.562 

21  0.138 0.055 0.004 0.041 0.134 0.260 

1  0.719 0.096 0.009 0.562 0.704 0.918 

2  0.669 0.089 0.008 0.465 0.670 0.841 

  0.588 0.028 0.001 0.532 0.588 0.641 

Conclusions 

 The aim of the research was to verify whether there appear significant inter-
actions between volatilities of the Central European CDS prices, suggesting that 
their price can be influenced not only by fundamentals, but also by expectations 
(sunspot event). To verify this, first univariate volatility models were estimated 
to check for the periods of volatility growth. Next, the Cheung-Ng test for non-
causality in variance was run, using the rolling-over approach and the test ver-
sion suitable for the small samples. The author was interested in revealing the 
possible sources of the volatility growth in case of the CDS prices in the three 
countries, in spring 2010. Usually the situation of volatility growth is associated 
with the occurrence of sunspot event. There may have been two sources of such 
contagion – either the global growth of risk aversion due to the Greek crisis, or 
the local turmoil caused by the worsening economic situation of Hungary.  
It appeared, however, that the moments in which the null hypothesis of non-



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 125

causality in the pairs including Hungary was not rejected, overlapped with the 
moment of Hungarian crisis in 2010.  It was also observed that the periods of 
higher volatility in Hungary did not have equivalents in Polish and Czech CDS 
volatility. Such situation can indicate that the investors do not expect the crisis 
outbreak in Poland or Czech Republic when it happens in Hungary and they do 
not assess the risk of investment in the whole Central Europe based upon the 
situation in the country of weaker fundamentals.  
 Eventually, yet anoher test for causality in variance was performed, through 
estimating bivariate stochastic volatility models with Granger  causality for 
each pair of instruments. The results are clear: there is a strong causality from 
Polish CDS volatility to the volatility of the rest CDS prices.  

 The increase in conditional volatilities of the instruments in spring 2010 can 
suggest that contagion did occur. However, according to the presented results, 
the source of it was outside the Central Europe. If there was a reaction to the 
turmoil in Hungary, it was not reflected in the volatilities of Polish and Czech 
CDS prices. Thus, the reaction of the CDS prices of Poland and Czech republic 
to the problems in Hungary was not noticeable. However, the fact that the 
events of causality appeared during the problems in Greece can suggest that 
expectations do play a role in CDS pricing. Since the Central Europe is not crit-
ically linked via fundamentals with the Southern one, the contagion which oc-
curred in May 2010 must be so called “expectations-driven”. 

 What is more, the results of the research show also that there exist causality 
linkages in the second moments of the CDS prices processes. Significant reac-
tions of volatilities of Czech and Hungarian CDS prices to the changes of the 
volatility of Polish CDS price were found. The linkages are in fact bilateral, but 
the causality from Poland is much stronger. On the other hand, the turnover on 
the Hungarian CDS market was the highest in the analysed period. The explana-
tion of the result can be the following – the sovereign CDS instruments are 
bought mainly for speculation. In the period over study Hungary was the most 
risky country from the region, and investments in Hungarian swaps could allow 
for the highest earnings. Thus, the investors were interested in trading these 
particular instruments. However, from the analysed markets, the Polish one is 
the biggest and if an investor wants to sell his assets in a Central European mar-
ket as quickly as possible, the easiest way is to trade them on the Polish stock 
exchange. This may explain the fact that – although the turnover on the Hungar-
ian CDS market was the highest –  the strongest causality in variance occurred 
from the Polish one. This conclusion could explain why the volatility of Polish 
and Czech CDS prices did not react to the Hungarian problems. 

  



Agata Kliber 126 

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Appendix 

Non-Causality test of Cheung and Ng 

Let us consider two stationary and ergodic time series processes: tX  and tY , as 

well as two information sets defined by: 1{ , 0}t tI X j   and 

{ , , 0}.t t j t jJ X Y j    tY  is said to cause 1tX   in variance if 



Sovereign CDS Instruments in Central Europe – Linkages and Interdependence 127

2 2
1 , 1 1 , 1[( ) | ] [( ) | ],t x t t t x t tE X I E X J        

where , 1x t  is the conditional mean of 1tX   (conditioned on tI ). Feedback in 

variance occurs when X causes Y, and Y causes X. Let us also suppose that: 
1/2

, ,

1/2
, ,

,

.

t x t x t t

t y t y t t

X h

Y h

 

 

 

 
 

 In the model above, ,z t  denotes conditional mean, ,z th  conditional vari-

ance, while t   and t  are white noise processes with null mean. Let tU  and tV  
denote squares of standardised residuals: 

22
,, 2 2

, ,

( )( )
, .t y tt x t

t t t t
x t y t

YX
U V

h h


 


     

Let , ( )U Vr k  denote cross-correlation between U and V, for the k-th lag: 

,
,

, ,

( )
( ) ,

( (0) (0))
U V

U V
U U V V

c k
r k

c c
  

where , ( )U Vc k denotes covariance between U and V at lag k. Since the processes 

U and V are independent: 

,

,

( ) 0 1 0
, , .

0 0 1( )

U V

U V

T r k
N k j

T r j

    
     

    
 

 Cheung and Ng (1996) proposed the following test to verify the causality in 
variance. First, we construct the following statistics: 

2
, ( ),

k

U V
i j

S T r i


  
 

which is distributed according to 2  distribution with (k-j+1) degrees of free-
dom. If the sample is small, the following, corrected version of the statistics is 
applied: 

2
, ( ),

k

i U V
i j

S T r i


  
 

where 
2

.
| |i

T

T i
 




  

 



Agata Kliber 128 

Multivariate Stochastic Volatility Model with Granger Causality  
of Yu and Meyer 

The model has the following form: 

,  ~ ( , ),t t t t iid y Ω ε ε 0 Σ  

1 2

2 2
1 ,( )  ~ (0, ( , )),t t t t iid diag       h μ Φ h μ η η  

where: 

1 2( , ) 'y yy denotes the mean-adjusted time series of data,  

t is a diagonal matrix ( (exp( )),
2
t

t

h
diagΩ  

1
,

1t






 

  
 

Σ
     

11 12

21 22

 = .
 
 
 
 
 

Φ  

Naturally, 1 2 1, 2, 1, 2, 1, 2,( , ) ', ( , ) ', ( , ) ', ( , ) '.t t t t t t t t th h        μ h ε η  

 In the model it is assumed that the (mean-adjusted) returns and volatilities 
are cross-dependent, as well as that the volatility of the first asset can be 
Granger-caused by the volatility of the second one, and that the volatility of the 
second asset can be caused by the volatility of the first one. In order to investi-
gate the direction of volatility spillovers we estimate the model and check the 
estimates of the parameters 12  and 21 .  

Zależności i powiązania między instrumentami CDS na dług rządowy  
w gospodarkach Europy Środkowej 

Z a r y s  t r e ś c i. Artykuł przedstawia badanie współzależności między procesami cen instru-
mentów CDS (credit default swap) w Europie Środkowej. Autorka analizuje zależności między 
zmiennościami cen instrumentów w okresie kryzysowym starając się znaleźć odpowiedź na pyta-
nie, czy ich cena determinowana jest w znacznym stopniu przez zależności regionalne i oczeki-
wania  inwestorów (zjawisko zarażania sterowane oczekiwaniami, ang. sunspot). Wyniki prze-
prowadzonego badania sugerują, że ceny instrumentów CDS są w znacznym stopniu sterowane 
oczekiwaniami (gwałtowna reakcja na kryzys grecki), jak również że zależności regionalne – 
mimo że istnieją – mają mniejszy wpływ na cenę kontraktów, niż wydarzenia ogólnoeuropejskie. 

S ł o w a  k l u c z o w e: wielowymiarowe modele zmienności, CDS, Europa Środkowa, przeno-
szenie zmienności, sunspot.  


