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© 2013 Nicolaus Copernicus University. All rights reserved.  
http://www.dem.umk.pl/dem 

D Y N A M I C  E C O N O M E T R I C  M O D E L S  
DOI: http://dx.doi.org/10.12775/DEM.2013.005  Vol. 13 (2013) 87−106 

Submitted October 21, 2013  ISSN 
Accepted December 30, 2013 1234-3862 

Agata Kliber, Barbara Będowska-Sójka*  

Economic Situation of the Country or Risk 
in the World Financial Market? The Dynamics  

of Polish Sovereign Credit Default Swap Spreads∗∗  

A b s t r a c t. In the article we examine what determines the Polish sovereign Credit Default 
Swap dynamics. We consider not only measures of changes of the economic situation of the 
country, but also the impact of the international data. We find that the dynamics of the Polish 
sCDSs is very vulnerable to the dynamics of exchange rates, stock indices and bond spreads. 
These variables allow us to explain its behavior without including variables reflecting eco-
nomic situation of the country. It is shown that the impact of information inflow is also im-
portant.  

K e y w o r d s: sovereign Credit Default Swap, Bond spread, Stock Exchange indices, ex-
change rates, sunspots, volatility transmission, volatility models, principal component analy-
sis, event analysis.  

J E L Classification: C22, G14, G32. 

Introduction  
 Credit derivatives were perceived as a successful financial innovation in 
the 90s. The most common type of credit derivatives are credit default swaps 

                                                 
* Correspondence to: Agata Kliber, Poznań University of Economics, Department of Ap-

plied Mathematics, Al. Niepodległości 10, 61-875 Poznań, Poland, e-mail: agata.kli-
ber@ue.poznan.pl; Barbara Będowska-Sójka, Poznań University of Economics, Department 
of Econometrics, Al. Niepodległości 10, 61-875 Poznań, Poland, barbara.bedowska-
sojka@ue.poznan.pl. 

∗∗ This work was partially financed by the Polish Ministry of Science and Higher Educa-
tion through the project number N N112 372340. 



Agata Kliber, Barbara Będowska-Sójka 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 

88

(CDS). In a credit default swap one party of the contract buys protection and 
pays the seller a fixed premium each period, until either default occurs or the 
swap contract matures. If a default occurs, the seller is obligated to buy back 
from the buyer the defaulted bond at its nominal value.   
 The sovereign credit default swaps (sCDS) are financial instruments 
perceived as a protection against insolvency on debt issued by the sovereign 
borrower (a country). The protection buyer pays a regular premium, the so-
called CDS spread.  
 During the financial crisis in 2008–2009 investors became concerned 
about the overall economic situation and as a result sCDS spreads rose 
sharply. The reason is that the price of the sCDS contracts is believed to 
represent the risk associated with the country. This is embedded in the nature 
of the contract, which can be interpreted as a bet on the country default or 
the “insurance” against the situation that the country would not pay its obli-
gations. If the risk associated with the country grows, the price of the “insur-
ance” must grow as well. CDS contract to some extent may be perceived as 
an insurance, although it differs in the sense that the protection buyer may 
receive the payment without suffering any loses. As from the start of global 
financial crisis sCDS spreads have risen substantially and then dropped al-
most to the initial level, of particular interest is if these changes of spreads 
are driven by real economic situation. 
 Usually the economic indicators are perceived as those that represent the 
economic situation of the country (see e.g. Kosmidou, 2008). However, most 
of the indicators are of monthly or quarterly frequency, while the sCDS in-
struments are traded daily. Therefore, researchers point out that the sCDS 
premia is very vulnerable to sunspots and expectations and it may not reflect 
the risk properly (see eg. Longstaff et al., 2005; Longstaff et al., 2011; Plank, 
2010). By sunspots we refer to extrinsic variables in the way that contagion 
is neither caused by the fundamentals deterioration nor by trade relation-
ships. Moreover, the models for sCDS with macro-factors as the explanatory 
variables are usually capable of explaining about 50% of the sCDS dynamics 
(see e.g. Plank, 2010). In the case of the Polish market such a model is pre-
sented in Kliber (2013b), where the monthly dynamics of sCDS premium is 
explained by the macro-data of monthly frequency.  
 In the literature sCDS spreads are highly related to bond spreads and 
stock prices. Giannikos et al. (2013) find that CDS market dominates other 
markets in terms of price discovery and that the role of stock market dimin-
ishes during the financial crisis. As in case of all other financial instruments, 
the sCDS premia may be also vulnerable to the macroeconomic events from 
the American economy (Longstaff et al., 2011). However macroeconomic 



Economic Situation of the Country or Risk in the World Financial Market?...   

DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 

89

announcements constitute only a part of all incoming information and are 
released on the monthly basis. Lamoureux and Lastrapes (1990) use trading 
volume as a proxy for information arrival time. As trading volume is observ-
able variable it may well provide an approximation of inflow of widely de-
fined information. 
 This paper contributes to the existing literature in a few aspects. First of 
all, we focus on the Polish financial market, which is usually neglected in 
literature. Secondly, we investigate jointly the influence of expectations and 
fundamentals in sovereign Credit Default Swap pricing. To examine this 
issue we consider proxies for domestic as well as outside-the-country “fun-
damentals” and we study also the impact of selected American macroeco-
nomic announcements together with information inflow measure. We focus 
our study on constructing a model where the explanatory variables could be 
of daily frequency and simultaneously account for the economic condition of 
the country. We examine whether the Polish sCDS premia could be treated 
as an indicator of the true risk of Polish economy. 
 The remainder of the paper is structured as follows: in Section 1 we 
show how fundamentals influence the sCDS spreads, in Section 2 we focus 
on role of expectations in sCDS pricing, while in Section 3 we concentrate 
on the impact of macroeconomic announcements. We consider Polish sCDS 
of 5 years maturity over the period March 1, 2008 to May 31, 2013. 

1. Interactions of the sCDS Spread with Variables Representing 
the Economic Situation of the Country (VAR-DCC Model) 

 Based upon the findings in the literature we decided to include in our 
dataset the following variables: bond spreads, exchange rate, stock-exchange 
index and trading volume of the index as a proxy for incoming information. 
We are aware of the fact that the variables should not be considered as fun-
damentals sensu stricto, since they themselves are prone to sunspot and ex-
pectations. However, taking into account data of monthly  frequency inevi-
tably would result in loss of information about sCDS dynamics, since the 
latter are traded daily. Such an approach was proposed in Kliber (2013b) – 
the author tested vulnerability of monthly sCDS changes and volatility to the 
changes of such quantities as: unemployment, real wages, government earn-
ings and expenditures, import, export, inflation, terms of trade, internal and 
external debt. The models were able to explain about 50% of the sCDS vari-
ability. This result is similar to ones documented for another economies (see 
eg. Longstaff et al., 2011). Thus, we decided to use data of daily frequency 



DYNAMIC

90

that refl
imperfe
 The
the CEI
yield of
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German
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(see Fig

Figure 1

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sCDS s
Eventua
Polish s
preted a
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are pron
variable
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German
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of them
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lect the chan
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First, we run
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Agata Klibe

C MODELS 13 (2

ges of econo

in the study 
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considered. 

rs German bo

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variables are
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Engle (2002)
esents the re

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2013) 87–106

omic situatio

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dowska-Sójka 

6 

n of Poland,

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ex as a repres
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the market (F

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spread by sub
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sentative one
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deled the log
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DELS 13 (2013

nformation c
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cators 

e Table 1. W
r to make the
agram (see F
nly sCDS cha
ained by the 
t that from a

anges in expe

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3) 87–106 

91

criterion, 
08b). We 
per equa-

 

We notice 
e picture 
igure 3). 
anges do 
changes 

all of the 
ectations 



Agata Kliber, Barbara Będowska-Sójka 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 

92

about future development of economic situation of the country (if we assume 
that such information are incorporated in bond prices, exchange rates and 
stock indices). 
 In the next step, we estimate the multivariate conditional variance model 
with dynamic correlation (Engle, 2002), DCC(1,1,1,1) model with Student 
distribution, for the residuals obtained from the VAR model. Estimation is 
done in two steps. First, we estimate univariate volatilities (GARCH mod-
els), and in the next step – the correlation equation. The estimation was run 
via OxMetrics6 software with package G@RCH (Laurent and Peters, 2002). 
The results of estimation are presented in Table 2. As we can see, all the 
variables (apart from trading volume) are significant in all equations. Also 
the average values of correlations are significant in the case of each pairs 
excluding the ones with volume. Absolute values of the correlations are ap-
proximately 0.4. In Figure 4 we present the obtained estimates of conditional 
correlations for each pairs apart from the ones including volume, while in 
Figure 5 – the estimates of conditional variances. 

2. Changes of Economic Situation in the World  
and Polish sCDS Pricing 

 In this Section we examine the vulnerability of Polish sCDS prices to the 
changes of similar indicators from the neighbor countries. Again, we take 
into account: bond spreads, exchange rates and stock exchange indices. 
In order to account for as much of the variability of the data as possible and 
to reduce the number of explanatory variables we decide to use Principal 
Component Analysis and check the reaction of Polish sCDS prices to the 
changes of the first principal components of each group of variables.  
 We calculate the bond spreads assuming again that the risk free rate of 
the region is represented by the German bonds yield.  Based upon the previ-
ous studies (Kliber, 2013a) we are aware of the fact that in the case of some 
countries such spreads in some periods appear to be negative. Hence, we 
excluded some of the countries from the analysis. Eventually, we took into 
account the following bond spreads: French and British (so called low-yield 
Western European countries), Spanish (Southern Europe), Swedish and 
Finnish (Northern Europe) and Hungarian one (Central Europe). The dynam-
ics of the spreads is presented in Figure 6. At the time of the study Hungary 
was the country of the highest bond spread, i.e. its risk was the highest 
among all analyzed countries, compared to the German bonds. We observe 
also a gradual growth of risk of Spain, which equaled the Hungarian one at 
the end of the studied period. Yields of bonds in France and UK are very low  



E

 

Figure 4

Figure 5

Economic Situa

.  Conditional 
WIG returns

.  Volatilities 
and returns o

ation of the Cou

correlations 
s and returns f

of CDS spre
of USD/PLN 

untry or Risk in 

DYNAMIC ECO

of CDS spre
from USD/PL

ead changes, b
exchange rate

the World Fina

ONOMETRIC MO

ead changes, 
LN exchange r

bond spread
e (DCC model

ancial Market?.

DELS 13 (2013

bond spread 
rate (DCC mo

changes, WIG
l) 

...   

3) 87–106 

93

 
changes, 

del) 

 
G returns 



DYNAMIC

94

compare
spread i
 The
that the
variance
tributed
Souther
countrie
 

Figure 6

 From
pean Un
dollar U
nent An
explana
of the 
SEK/PL
 Fina
and S&
and the 
ance (se
 We 
transmis
stock ex
sions.  

 ECONOMETRIC

ed to Germa
is occasional
e results of P
e first princip
e of the syst

d to Spain, 
rn Europe ha
es. 

.  Bond spread

m the exchan
nion: EUR/P

USD/PLN (se
nalysis in Tab
atory power, 

system. Th
LN – that is t
ally, we ana

&P500 (see F
first compo

ee Table 5).  
conclude th

ssion from a
xchange ind

Agata Klibe

C MODELS 13 (2

an bonds, wh
lly even nega
CA on bond
pal compone
tem. The hi
France and 
ad indeed a

ds of the selec

nge rates we
PLN, GBP/P
ee Figure 7).
ble 4. In this
since it was

he highest 
the EU curre
alyse four sto
Figure 8). Th
onent was ab

hat the bond
all of the an

dices are stro

er, Barbara Będ

2013) 87–106

hile in the N
ative.  
d spreads are
ent explained
ghest loadin
Finland, wh

an impact on

cted European

 choose the m
PLN, SEK/P
. We present
s case the fir
s able to exp
loadings ha
ncies. 
ock exchang
heir dynamic
ble to explain

d spreads are
nalyzed indic
ongly affecte

dowska-Sójka 

6 

Northern Eur

presented in
d only about
ngs in the fir
hich sugges
n the volatil

countries 

most represe
PLN as well
t the results 
rst componen
plain 55% of 
ave EUR/PL

ge indices: C
cs at that tim
n already 75

e the most i
cators of da
ed by comm

ropean coun

n Table 3. W
t 40% of the
rst compone
ts that the 

lity of the E

entative for th
 as the pric
of Principal 
nt has much 
f the overall 
LN, GBP/PL

CAC40, DAX
me was quite
5% of comm

immune to v
ily frequenc

mon shocks tr

ntries the 

We notice 
e overall 
ent is at-
crisis in 

European 

 

he Euro-
e of US 
Compo-
stronger 
variance 
LN and 

X, BUX 
e similar, 
mon vari-

volatility 
cy, while 
ransmis-



E

Figure 7

 Afte
we run 
In the f
plained 
we add 
we add 
subsecti
embedd
the mod
assumin
the sam
case of 
ables in
first pri
equation
tility eq
lagged 
between
compare
formatio
els with
that the 

Economic Situa

.  Exchange 
SEK/PLN an

er computing
the series of

first model w
by the histor
the PC1s as
 the explana
ion (Model 

ded. The resu
dels are esti
ng that the ω 

mple. In all c
the conditio

n the form of
incipal comp
n at their cur

quation are th
changes of 

n the sCDS c
e the models
on criteria. W
h lower numb

explanatory

ation of the Cou

rates of cu
nd USD/PLN

g the first pri
f ARMA-GA
we assume t
rical values o
s the explana
atory variab
2). In the th

ults of the es
imated via th
(see equatio

cases the val
onal mean eq
f lagged retur
ponent of bo
rrent values)
he squared l
bond spread

changes and b
s on the bas

We follow th
ber of explan
 variables ar

untry or Risk in 

DYNAMIC ECO

urrencies: E
N 

incipal comp
ARCH mode
that changes 
of the spread
atory variabl
les used in 
hird model (
timation are 
he so called

on 1) is equal
lues of this p
quation, we 
rns (the exce
ond spreads
, while the e

lagged return
d, however i
bonds’ sprea

sis of the log
he Schwarz cr
natory variab

re not redund

the World Fina

ONOMETRIC MO

UR/PLN, G

ponents of ea
els (see mod

of Polish s
d only (Mode
es (Model 1
VAR mode

(Model 3) th
presented in

d variance-ta
l to the unco
parameter ar
introduced t
eption is the 
, which are 

explanatory v
ns. In the fir
it appeared 
ad changes ar
g-likelihood 
riterion, sinc
bles and hen

dant.  

ancial Market?.

DELS 13 (2013

GBP/PLN, H

ach group of
del (1) in Ap
CDS are can
el 0). In the n
). In the thir

el from the p
he previous 
n table 6. In 
argeting met
nditional var
re very smal
the explanato
bond spread
introduced 

variables in t
rst step we u
that the inte
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ce it prefers t
nce we could

...   

3) 87–106 

95

 
HUF/PLN, 

f factors, 
ppendix). 
n be ex-
next one, 
rd model 
previous 
two are 

all cases 
thod, i.e. 
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ll. In the 
ory vari-
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into the 
the vola-
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eous. We 
d the in-
the mod-
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DYNAMIC

96

Figure 8

 The
terion) i
by princ
Change
spreads 
spread. 
exchang
change 
nificant 
expect t
the USD
PC1-exc
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pal com
Thus, in
need an
drives t
Europea

3. Imp
 The
differen
market 

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.  Stock Excha
axis) 

e best model 
is the most g
cipal compon
s of the spre
of the neigh
Additional s

ge rates and
rate. In the 

t variable is 
the special r
D/PLN rate i
change-rate 
would like t

mponents outp
n order to exp
ny variables r
the dynamic
an countries,

act of the A
e literature o
nt financial in
(see e.g. Ed

Agata Klibe

C MODELS 13 (2

ange indices: 

(taking into 
general one –
nents) and in
ead can be th
hbour countr
significant ex

d stock exch
case of the 
the lagged s

role of US ec
s present in t
component, 
to stress the 
performed th
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representing 
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Announcem
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nstruments is
erington, Le

er, Barbara Będ

2013) 87–106

CAC, DAX, 

account the
– it includes 
ndicators of t
hus explaine
ries, as well 
xplanatory v

hange indices
conditional 

squared valu
conomy on t
the explanato
and as the U
fact that the 
he model inc
namics of the
the econom

sk indicator 
he risk of Am

ments from
of macro n

s huge and in
ee, 1993), for

dowska-Sójka 

6 

S&P (main ax

e log-likeliho
both the env
the country‘

ed by the cur
as the chang

variables are 
s, as well as
variance equ

ue of WIG r
the risk perc
ory variables

USD/PLN exc
model inclu

cluding the “
e Polish sCD

mic situation o
is the risk 

merican econ

m the Ame
news on retu
ncludes surv
reign exchan

xis), and BUX

ood and Schw
vironment (ex
s economic s
rrent change 
ge of domes
the lagged v
s the USD/P
uation, the o
returns. We 
ception of Po
s in two form
change rate. 

uding only th
“domestic” v
DS we actuall
of the countr
perception 

nomy. 

rican Mark
urns and vola
eys concerni
nge market (

 
X (second 

warz cri-
xpressed 
stability. 
of bond 

stic bond 
values of 
PLN ex-
only sig-
can thus 
oland, as 

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ly do not 
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of other 

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atility of 
ing bond 
(e.g. An-



Economic Situation of the Country or Risk in the World Financial Market?...   

DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 

97

dersen, Bollerslev, 1998) and equity market (e.g. Będowska-Sójka, 2011). 
Longstaff et al. (2005) confirm the impact of macroeconomic measures of 
bonds liquidity on CDS spreads. We examine to what extent are sCDS sensi-
tive to macro news announcements and information flow to the market. 
Therefore, we use seven macro releases commonly used in the literature of 
macro news announcements effect (e.g. Almeida et al., 1998; Będowska-
Sójka, 2011). These are: industrial production, retail sales, consumer confi-
dence, durable goods order, unemployment rate, producer price index, new 
home sales and purchasing manager index. These announcements are aggre-
gated into indicator variable (DV) taking value of 1 if at least one release 
occur within the day and zero otherwise. The data considering macro an-
nouncements are from www.bankier.pl. 
 As a measure of intensity of unobservable information arrival we use 
trading volume of WIG index (Lamoureux, Lastrapes, 1990). We assume 
that information arrival may influence the sCDS spreads. However, we are 
aware of the fact that in some cases trading volume cannot be an accurate 
proxy for information arrival. It refers to the liquidity motivated trading ac-
tivities, heterogeneity among traders’ expectations and beliefs etc. (see 
Kalev et al., 2004). By incorporating lagged trading volume into the condi-
tional volatility equation of the FIGARCH(1,d,1) model we examine if the 
rate of news arrivals significantly influence the conditional volatility.  
 We model sCDS return series, rt, with AR(1)-FIGARCH (1,d,1) process 
(see Appendix 2). We introduce into the conditional variance equations indi-
cator variable standing for aggregated macro announcements. Dummy varia-
ble, DVt, has a value of 1 at the day of macro announcements and zero oth-
erwise. This variable is responsible for the impact of the macro releases on 
the conditional volatility. If there is any influence of these macro releases, 
the estimated parameter should be significant. In another model we introduce 
the lagged volume, VOLt-1, into the conditional variance equation in order to 
account for undefined information. The significance of the parameter stand-
ing by the volume variable would suggest that information inflow affect 
sCDS volatility. The FIGARCH model is chosen from the GARCH class 
models – the choice is based on information criteria and the value of loga-
rithm of likelihood function.  
 The results of model estimation are shown in Table 7. The impact of 
macro news is not significant. However, the lagged stock index volume vari-
able appeared to be significant. It suggests that overall activity driven at least 
by incoming information or the rate of news arrivals are influencing sCDS 
premia’s volatility significantly.  



Agata Kliber, Barbara Będowska-Sójka 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 

98

 Parameters are stable across different specifications. When included in 
the equation, the lagged volume causes substantial reduction in the value of 
the constants’ parameter in the conditional variance equation. However, both  
α and β do not change substantially. Thus sCDS returns are not sensitive to 
the examined public macro announcements, but they are to some extent in-
fluenced by unspecified information. 

Conclusions 
 In the paper we analyzed dynamics of Polish sovereign Credit Default 
Swaps and checked its reaction to the changes of variables reflecting eco-
nomic situation of the country, as well as the ones connected with economic 
situation in the world financial markets. In order not to replicate our previous 
findings, as well as not to lose too much information, we did not consider the 
actual fundamentals (of monthly or quarterly frequency), but concentrated 
on the variables from financial markets, such as bonds, exchange rates and 
stock indices. We compared the models that included the “domestic” varia-
bles with the ones including the analogous variables from neighborhood 
countries.  
 We found that although the variables reflecting the economic situation of 
the country play a significant role in explaining the dynamics of the sCDS 
premia, the model that take into account only the environment variables is 
capable to explain the dynamics of the premia even better. Both the ex-
change rates and bond spreads have a strong explanatory power in explain-
ing the sCDS premia. We find also that the impact of important macro news 
from the American economy on the dynamics of the sCDS premia is insig-
nificant. However, we show that the impact of information inflow proxied by 
trading volume is strong. 
 Taking into account the findings presented in the paper, we doubt 
whether the premium of the Polish Sovereign Credit Default Swaps should 
be treated as the risk indicator of the Polish economy. Moreover, the results 
of the research suggest that the links among some segments of world finan-
cial markets can be stronger than the links among these segments within one 
country. 

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Plank, T. (2010), Do Macro-Economic Fundamentals Price Emerging Market Sovereign CDS 
Spreads?, Working Paper: http://finance.wharton.upenn.edu/weiss/wpapers/2010/10-
5.pdf, (10.06.2013). 

Sytuacja gospodarcza kraju, czy oczekiwania? Co decyduje  
o dynamice polskich kontraktów CDS? 

Z a r y s  t r e ś c i. W artykule dokonano analizy dynamiki  kontraktów CDS (Credit Default 
Swap – instrumentów zamiany ryzyka kredytowego) wystawianych na polskie euroobligacje. 
Badanie dotyczy okresu 2008-2013. Celem badania jest określenie, czy na dynamikę kontrak-
tów wpływ mają wydarzenia międzynarodowe, czy też krajowe, a w rezultacie, czy spread 
kontraktów, interpretowany jako wskaźnik ryzyka danego kraju, faktycznie to ryzyko od-
zwierciedla. Na podstawie uzyskanych wyników można stwierdzić, że do opisu dynamiki 
i zmienności kontraktów CDS wystarczy model ze zmiennymi reprezentującymi ryzyko 
krajów sąsiadujących, nie uwzględniający wielkości związanych z jego gospodarką. 

S ł o w a  k l u c z o w e: CDS, obligacje, indeksy giełdowe, kurs walutowy, zmienność, 
przenoszenie zmienności, analiza zdarzeń.  
 
  



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Appendix 1 – Tables 

Table 1.  Estimates of the unrestricted VAR model for Polish sCDS, bond spread, 
exchange rate, WIG and its volume 

Dependent variable Explanatory variable Coeff. Standard error 
CDS  

 CDS(–1) 0.0011 0.0359 
 WIG(–1) –0.3740 0.1062 
 VOL(–1) –0.0029 0.0022 
 bond(–1) 0.2365 0.0571 
 plnusd(–1) –0.0004 0.1110 
 const –0.0006 0.0012 

WIG    
 CDS(–1) 0.0078 0.0121 
 WIG(–1) 0.0790 0.0358 
 VOL(–1) –0.0014 0.0007 
 bond(–1) –0.0408 0.0193 
 plnusd(–1) –0.0131 0.0375 
 const 0.0004 0.0004 

Volume (WIG)    
 CDS(–1) 0.3037 0.4480 
 WIG(–1) 0.8220 1.3266 
 VOL(–1) –0.3923 0.0272 
 bond(–1) 0.1560 0.7137 
 plnusd(–1) –2.8653 1.3867 
 const 0.0004 0.0146 

bond spread    
 CDS(–1) –0.0060 0.0220 
 WIG(–1) 0.1329 0.0651 
 VOL(–1) –0.0010 0.0013 
 bond(–1) 0.0910 0.0350 
 plnusd(–1) 0.0277 0.0681 
 const –0.0003 0.0007 

PLN/USD    
 CDS(–1) –0.0240 0.0108 
 WIG(–1) 0.1525 0.0319 
 VOL(–1) 0.0007 0.0007 
 bond(–1) –0.0669 0.0172 
 plnusd(–1) –0.2078 0.0333 
 const –0.0003 0.0004 

Note:  the bolded parameters are statistically significant at α=0.05. CDS(–1) denotes the lagged change of 
CDS, WIG(–1) – lagged change of WIG, VOL(–1) – lagged volume, bond(–1) – lagged change of bond, 
plnusd(–1) – laggech change of exchange rate, while const – a constant. 



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Table 2.  Estimates of the DCC–Engle model – univariate GARCH models and con-
ditional correlations 

Variable Coefficient Std.Error 
CDS   

ω x 10^4 0.3946 0.1872 
α 0.1082 0.0301 
β 0.8680 0.0304 

WIG   
ω x 10^4 0.0103 0.0052 

α 0.0674 0.0128 
β 0.9259 0.0130 

Volume   
ω 0.0098 0.0114 
α 0.0536 0.0362 
β 0.9062 0.0808 

Bond spread   
ω x 10^4 0.1408 0.0582 

α 0.0885 0.0217 
β 0.8878 0.0254 

Exchange rate   
ω x 10^4 0.0217 0.0103 

α 0.0705 0.0208 
β 0.9123 0.0230 

Correlations   
ρ_(CDS, WIG) –0.4638 0.0350 

ρ_(CDS, volume) –0.0081 0.0449 
ρ_(CDS, bond) 0.4456 0.0359 
ρ_(CDS, exR) –0.4216 0.0364 

ρ_(WIG, volume) 0.0145 0.0440 
ρ_(WIG, bond) –0.4154 0.0363 
ρ_(WIG, exR) 0.3613 0.0388 

ρ_(volume, bond) 0.0036 0.0415 
ρ_(volume, exR) 0.0031 0.0437 
ρ_(bond, exR) –0.3329 0.0377 

a 0.0160 0.0040 
b 0.9554 0.0154 
df 11.1557 1.1568 

Note: the bolded parameters are statistically significant at α=0.05. All the parameters named according to 
Formulas (3) and (4) in Appendix 2. 

  



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Table 3.  Principal Component Analysis – bond spread. Components loadings and 
explanatory power of the variance of the system 

PC1  PC2  PC3  PC4  PC5  PC6  
HU.spread 0.3204 –0.4507 –0.7563 0.0408 –0.3473 –0.0056 
ESP.spread 0.5082 –0.1212 –0.0171 0.1036 0.6836 –0.4987 
FR.spread 0.5409 –0.1180 0.2363 0.1014 0.1367 0.7802 
UK.spread 0.1981 0.7156 –0.2518 0.6077 –0.1260 –0.0097 

SVE.spread 0.3007 0.5036 –0.2166 –0.7796 0.0033 0.0341 
FI.spread 0.4657 –0.0503 0.5114 –0.0140 –0.6144 –0.3759 

Standard deviation  1.5202  1.045  0.9043  0.8842  0.77257  0.63295  
Proportion of Variance  0.3852  0.182  0.1363  0.1303  0.09948  0.06677  
Cumulative Proportion  0.3852  0.5672  0.7035  0.8337  0.93323  1  

Note: first component explained only about 40% of the system variance. HU.spread denotes spread of 
Hungarian bonds, ESP – the Spanish ones, FR– the French ones, UK – the British ones, SVE – the Swe-
dish ones, while FI – the Finnish ones. 

Table 4.  Principal Component Analysis – exchange rates. Component loadings and 
explanatory power of the variance of the system 

PC1  PC2  PC3  PC4  PC5  
eurpln  0.5531  –0.0157  0.1965  –0.1719  –0.7910  
gbppln  0.5140  –0.1654  0.3073  –0.5496  0.5585  
hufpln  0.2960  0.7208  –0.5928  –0.1847  0.0856  
sekpln  0.4946  0.1695  0.2425  0.7835  0.2324  
usdpln  0.3124  –0.6512  –0.6758  0.1432  0.0324  

Standard deviation  1.6563  0.985  0.8267  0.6385  0.44174  
Proportion of Variance  0.5487  0.1941  0.1367  0.08154  0.03903  
Cumulative Proportion  0.5487  0.7428  0.8794  0.96097  1  

Note: first component explained almost 55% of the system variance. The eurpln denotes the exchange rate 
of euro, gbppln – of British pound, hufpln – of Forint, sekpln – of Sweden, while usdpln – the American 
one. 

Table 5.  Principal Component Analysis – stock exchange indices. Component load-
ings and explanatory power of the variance of the system 
   PC1  PC2  PC3  PC4  

BUX  –0.4351  0.8218  –0.3677  0.0113  
CAC  –0.5448  –0.0776  0.4497  –0.7035  
DAX  –0.5455  –0.1052  0.4323  0.7103  
S&P  –0.4651  –0.5546 –0.6897  –0.0196  

Standard deviation  1.737  0.7495  0.6061  0.2347  
Proportion of Variance  0.754  0.1404  0.0918  0.0138  
Cumulative Proportion  0.754  0.8944  0.9862  1  

Note: first component explained over than 75% of the system variance. BUX denotes the Hungarian stock 
exchange index, CAC – the French one, DAX – the German one, while S&P – the American Standard 
and Poor’s. 



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DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 

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Table 6.  Estimates of ARMA–GARCH Models of the dynamics of Polish sCDS 
spread (model 0–4) . 

model 0 model 1 model 2 model 3 
 Variable Coeff. Std.Error Coeff. Std.Error Coeff. Std.Error Coeff. Std.Error 
CondME 
PCbond, t 0.116 0.009 0.095 0.010 
PCex, t–1 0.177 0.069 0.253 0.080 
PCin, t–1 0.148 0.037 0.159 0.036 
Bondt  0.503 0.056 0.198 0.045 
WIGt–1  –0.387 0.072 
ERt–1 0.176 0.083 

CVarEq 
(PCex, t–1)2 0.367 0.097 

Vol t–1 0.000 0.001 
(WIGt–1)2 0.390 0.133 0.486 0.123 
(Bondt–1)2  –0.001 0.022 

α 0.110 0.002 0.100 0.022 0.090 0.022 0.088 0.020 
β 0.842 0.030 0.841 0.030 0.836 0.033 0.828 0.029 

DF 4.230 0.388 4.218 0.366 4.258 0.418 4.332 0.402 
ω 0.001 0.002 0.002 0.002 
LL 2301 2460 2403 2481 

LL ratio 
(mod. 0) 0.000 0.000 0.000 
LL ratio 
(mod. 3) 0.000 0.000 0.000 

Note: PCbond,t stands for first principal component in PCA for bond spreads. PCex, t–1 for exchange rates 
with lagged values, and PCin, t–1 for stock indices with lagged values. Bondt stands for domestic bond 
spread changes, WIGt–1 is lagged value of WIG returns, ERt–1 describes lagged returns of USD/PLN 
exchange rate, and Volt–1 is lagged value of trading volume of WIG index. Based upon the LL–ratio test 
we conclude that each of the models: 1, 2, 3 outperform the Model 0, while Model 3 outperforms all of 
the models: 0, 1 and 2. The bolded parameters are statistically significant at α=0.05. 

 Table 7. Estimates of Model 4: AR(1)–FIGARCH(1,d,1) model of the dynamics of 
Polish sCDS spread with macro news and trading volume variables 

  Coeff. Std.err. Coeff. Std.err. Coeff. Std.err. 
AR(1) 0.1017 0.0315 0.1000 0.0315 0.0979 0.0333 
ω*104 306.8671 51.9121 289.8801 36.5562 262.7081 22.7071 
DVt   –0.0001 0.0001   

Volt–1*104     2.4900 0.0359 
d 0.7570 0.0452 0.7510 0.0461 0.7584 0.0444 
α 0.0656 0.1051 0.0629 0.1020 0.0589 0.1104 
β 0.7144 0.0587 0.7100 0.0599 0.7349 0.0548 
df 3.2024 0.2381 3.2201 0.2436 3.1553 0.2245 
LL 2311.7111  2312.3212  2313.1121  

LL ratio test   0.27  0.09  
Note: Volt–1 is lagged value of trading volume of WIG index. DVt is an indicator variable standing for 
aggregated macro announcements The bolded parameters are statistically significant at α=0.05. 



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105

Appendix 2 – The models 
ARMA–GARCH MODEL (Bollerslev, 1986) with explanatory variables. 
Let us denote by ty  the value of the process at time t. The following model: 

1 1 1

2 2 2

1 1 1

,

,

,

m n t

t i t i j t j t k
i j k

t t t
p q r

t i t i j t j k
i j k

r a r b y y z

y

y w

σ ε

σ ω α β σ

− −
= = =

− −
= = =

= + + +

=

= + + +

∑ ∑ ∑

∑ ∑ ∑

 (1) 

is called an ARMA–GARCH model with explanatory variables iz and jw .  

We assume that tε is an iid process of mean 0 and unit variance. Moreover, 
0, 0, 0.i iω α β> ≥ ≥  

In Section 3 we use AR(1)–FIGARCH(1,d,1) model with specification given 
by Chung (1999): 

 1 1 , ,t t t t t tr r y yϕ σ ε−= + =   
  2 2 2 2

,( )(1 ) ( ) [1 ( )]( ),d
t i t i tL L y L yα σ β σ− − = − −  (2) 

where: ∑∑
==

−=Β−=Α
p

i

i
i

q

i

i
i LLLL

11
1)(,1)( βα , a 10 ≤≤ d  is fractionally in-

tegrated parameter. 

THE DCC MODEL (Engle, 2002). 
Let us denote by ty the value of the process at time t. Let us assume also 
that: 

1| ~ ( , ),
,

Ft t t

t t t t

y N−

=

0 H
H D R D

 (3) 

where: 

 

11, ,

2
, , , ,

1 1

1/2 1/2

'

1 1 1 1

( ,..., ),

,  1,..., ,

( ( ) ( ( )) ,

1 .

t t kk t

q p

ii t i t ij i t j ij ii t j
j j

t t t t

M N M N

t m n m t m t m n t n
m n m n

diag h h

h y h i k

R diag diag

a b a b

ϖ α β− −
= =

− −

− − −
= = = =

=

= + + =

=

⎛ ⎞
= − − + +⎜ ⎟
⎝ ⎠

∑ ∑

∑ ∑ ∑ ∑

D

Q Q Q

Q Q u u Q

 (4) 



Agata Kliber, Barbara Będowska-Sójka 

DYNAMIC ECONOMETRIC MODELS 13 (2013) 87–106 

106

The vectors tu  are k–dimensional and , ,/it i t ii tu y h= .The k–dimensional 

matrix Q  is the unconditional covariance matrix of .tu It is also assumed 

that the scalars ma and nb are non–negative and 
1 1

1.
M N

m n
m n

a b
= =

+ <∑ ∑  

 In our study we estimated the model with Student distribution, i.e. we 
assumed that:  

1| ~ ( , , ),Ft t ty t ν− 0 H  
where  ν denotes degrees of freedom. The value of this parameter is estab-
lished through estimation. When 2ν > , then tH exists and is interpretable as 
a conditional variance matrix. 
 The model was estimated using the two–step procedure. First, the Q was 
estimated as the unconditional correlation matrix of .tu  Then, the parame-
ters a and b were estimated by Gaussian quasi maximum likelihood. 
Bollerslev and Wooldridge (1992) showed that even in the case when data 
generating process is not conditionally Gaussian, we can obtain a consistent 
estimator using the Gaussian quasi maximum likelihood. For more details 
considering estimation in G@RCH package see eg. (Laurent et al., 2012). 
 

  




