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

Małgorzata Doman 
Poznań University of Economics 

Ryszard Doman 
Adam Mickiewicz University in Poznań 

The Impact of the Exchange Rate Dynamics  
on the Dependencies in Global Stock Market†                                        

A b s t r a c t. The paper addresses the question of how the exchange rate dynamics affects the 
analysis of linkages between national stock markets. We consider  two ways of tackling the prob-
lem. The first one consists in denominating the analyzed quotations in the same currency. The 
second deals with a direct introducing the exchange rate into a model. Our analysis is based on 
the daily return series on selected stock indices from the period 1995-2010. We model the de-
pendence structure using dynamic copulas. This allows us to separate the dynamics of depend-
ence from the volatility dynamics. 

K e y w o r d s: stock market, stock index, linkages, denomination, exchange rate, copula.   

Introduction  

 The knowledge about linkages between stock markets is of importance in 
risk management and building investment strategies. Moreover, it is crucial for 
understanding the nature of global financial market. It is thus quite natural that 
there exist many papers dealing with this problem. Most of them belong to the 
contagion literature. The most popular approach here is to denominate the indi-
ces (or other stock market quotations) in local currencies (Eun and Shin, 1989; 
Koutmos, 1992; Theodossiou and Lee, 1993; Wong et al. 2004). The next popu-
lar choice is denomination in the US dollar (e.g. Karolyi and Stulz, 1996; Ro-
driguez, 2007)).  There exist analyses performed both in a local currency and 
the US dollar (e.g. Lee et al., 2001). Chen and Poon (2007) use local currency 
for indices in the case of developed markets and for emerging market they use 
US dollar denominated indices. Veiga and McAleer (2004) remarked that the 
                                                 

† This work was financed from the Polish science budget resources in the years 2010-2013 as 
the research project N N111 035139. 



Małgorzata Doman, Ryszard Doman 74

use of the US dollar as a common currency is a complicating factor. This is 
because in such situation the US market is always included in the empirical 
analysis. Changes in the US dollar are largely influenced by changes in US fun-
damentals, which also drive financial returns. Thus, it is likely that some of the 
co-movements observed among returns in different markets expressed in 
a common currency are caused by changes in the fundamentals driving the US 
dollar exchange rate. However, the findings by Veiga and McAleer (2004) 
based on quite extensive analysis of the sensitivity of spillover effects on de-
nomination show that the denomination has no significant impact on the results.  

 In the paper, we ask how introducing the exchange rate dynamics influences 
the dynamics of linkages between stock indices. We consider dependencies 
between the elements of each pair of indices from the triple: the S&P500, the 
DAX and the WIG20 (the main index of the Warsaw Stock Exchange). In addi-
tion, we investigate the linkages between the DAX and the NIKKEI225. The 
analysis of linkages is performed by means of a DCC-copula model. We esti-
mate dynamic copula correlations between the daily returns on the indices de-
nominated in local currencies and in chosen alternative currencies.  

 The aim of the presented investigation is to analyze the sensitivity of the 
dynamic copula correlation estimates to the denomination of the indices in al-
ternative currencies. In the case of the S&P500 and the DAX, the considered 
currencies are the US dollar and the euro. The analysis for the S&P500 (or the 
DAX) and the WIG20 includes denomination in the US dollar, the euro and the 
Polish zloty. For the pair DAX and NIKKEI225, the denominations in the US 
dollar, the Japanese yen and the euro are included. Moreover, for each of the 
considered pairs of the indices we calculate the dynamic copula correlations 
based on a three-dimensional  DCC-copula model estimated jointly for the indi-
ces denominated in local currencies and the corresponding exchange rate 
(USD/EUR for SP500-DAX, USD/PLN for SP500-WIG20, EUR/PLN for 
DAX-WIG20, and EUR/JPY for DAX-NIKKEI225).  

1.  DCC-Copula Models  

 Modeling the dependencies between financial returns is a difficult task be-
cause of special properties of  these series.  Typical return series usually exhibit 
conditional heteroskedasticity, different types of asymmetries and structural 
breaks which strongly influence estimation results for models of the dependence 
structure. Moreover, the dynamics of dependencies significantly changes in 
time. For example, it is well documented in many studies that dependence be-
tween returns on different assets is usually stronger in bear markets than in bull 
markets (Ang and Bekaert, 2002; Ang and Chen, 2002; Patton, 2004). This ex-
ample of asymmetric dependence in financial markets is of great importance for 
portfolio choice and risk management. The main problem connected with this 
phenomenon is, however, that from the theoretical point of view the mentioned 



The Impact of the Exchange Rate Dynamics on the Dependencies…   75

asymmetry cannot be produced by a statistical model for the returns that as-
sumes an elliptical multivariate conditional distribution, and thus applying the 
linear correlation is not justified. An alternative concept that allows for model-
ing the dependence in a general situation is copula.  

 Roughly speaking, a d-dimensional copula is a mapping ]1 ,0[]1 ,0[: dC   
from the unit hypercube into the unit interval which is a distribution function 
with standard uniform marginal distributions.  

 Assume that  ),,( 1 dXXX    is a d-dimensional random vector with joint 

distribution F and marginal distributions iF , di ,,1 . Then, by a theorem by 
Sklar (1959), F can be written as: 

))(,),((),,( 111 ddd xFxFCxxF   .  (1)                                                 

 The function C is unique if iF  are continuous. Otherwise,  C  is uniquely 
given by: 

 ))(,),((),,( )1(
1

)1(
11 ddd uFuFFuuC   , (2)  

for ]1 ,0[iu , where })(  :inf{)(1
iii uxFxuF  . In that case, C is called the 

copula of F or of  X. Since the marginals and the dependence structure can be 
separated, it makes sense to interpret C as the dependence structure of the vec-
tor X. We refer to Patton (2009) and references therein for an overview of  fi-
nancial time series applications of copulas. There one can also find more infor-
mation about advantages and limitations of copula-based modeling.   

 The simplest copula is defined by dd uuuuC   11 ),,( , and it corre-
sponds to independence of marginal distributions. The next two important ex-

amples are ),,min(),,( 11 dd uuuuC   , and, in the two-dimensional case, 

)0 ,1max(),( 
jiji uuuuC . The first corresponds to comonotonicity or 

perfect dependence (one variable can be transformed almost surely into another 
by means of an increasing map), and the second, to countermonotonicity or 
perfect negative dependence of the variables iX  and jX (one variable can be 

transformed almost surely into another by means of a decreasing map). In the 
empirical part of this paper we will use the Student t copula. It is defined as 
follows: 

))(,),((),,( 1
1

1
,1, d

d
d

St ututtuuC    RR ,  (3) 

where R,t denotes the d-dimensional Student’s t distribution with   degrees of 

freedom and correlation matrix R, and t  stands for 1-dimensional Student’s 

t distribution with   degrees of freedom. In the bivariate case we will use the 

notation tC  ,  where  stands for correlation coefficient. 



Małgorzata Doman, Ryszard Doman 76

 The density associated to an absolutely continuous copula C  is a function 
c defined by: 

d

d
d

d uu

uuC
uuc








1

1
1

),,(
),,( .  (4) 

For an absolutely continuous random vector, the copula density c  is related to 
its joint density function h  by the following canonical representation: 

  )()())(,),((),( 11111 ddddd xfxfxFxFcxxf   , (5) 

where dFF ,,1   are the marginal distributions, and dff ,,1   are the marginal 
density functions.  

 In the case of non-elliptical distributions, measures of dependence that are 
more appropriate than the linear correlation coefficient are provided by two  
important copula-based tools known as Kendall’s tau and Spearman’s rho (Em-
brechts et al., 2002). Since the dynamics of Kendall’s tau can be easily derived 
for the results presented in this paper, we recall suitable definitions. If ),( YX  is 

a random vector and )~,~( YX is an independent copy of ),( YX  then Kendall’s 

tau for ),( YX  is defined as: 

  }.0)~)(~{(}0)~)(~{(),(  YYXXPYYXXPYX  (6) 

Thus Kendall’s tau for ),( YX  is the probability of concordance minus the 

probability of discordance. If ),( YX  is a vector of continuous random variables 
with copula C, then: 

1),(d),(4),(
2]1,0[ 

  vuCvuCYX .  (7)  

For the Student t copula tC  , , Kendall’s tau equals )arcsin(
2 


. 

 A very important concept connected with copula, relevant to dependence in 
extreme values, is tail dependence (Nelsen, 2006). If X and Y are random varia-
bles with distribution functions F and G then the coefficient of upper tail de-
pendence is defined as follows: 

))(|)((lim 11
1

qFXqGYP
qU




  ,  (8) 

provided a limit ]1,0[U  exists. Analogously, the coefficient of lower tail 
dependence is defined as: 

))(|)((lim 11
0

qFXqGYP
qL




  ,    (9) 

provided that a limit ]1,0[L  exists. If ]1,0(U  ( ]1,0(L ), then X and Y are 
said to exhibit upper (lower) tail dependence. Upper (lower) tail dependence 



The Impact of the Exchange Rate Dynamics on the Dependencies…   77

quantifies the likelihood to observe a large (low) value of  Y given a large (low) 
value of  X. The coefficients of tail dependence depend only on the copula C of 
X and Y: 

q

qqC
qL

),(
lim

0
 , 

q

qqC
qU

),(ˆ
lim

0
   (10)                                                

where )1,1(1),(ˆ vuCvuvuC  . For the Student t copula StC  , , the coef-

ficients of upper and lower dependence are both equal to 
 )1/()1)(1(2 1  t  (see McNeil et al., 2005).  

 Introduced by Patton (2004), the notion of conditional copula allows to ap-
ply copulas to modeling the joint distribution of tr conditional on information 

set 1t , where ),,( ,,1  tdtt rr r is a d-dimensional vector of financial returns. 

In this paper we consider the following general conditional copula model:  

)|(  ~|,),|(  ~| 1,1,1,11,1   ttdttdtttt FrFr  , (11)                                               

)|(~| 11   tttt Fr ,  (12)                                                

)|)|(,),|(()|( 11,,1,1,11   tttdtdttttttt rFrFCrF  ,
 
 (13) 

where the set t  includes the up to time t information on the returns on both 

considered financial assets, and tC  is the conditional copula linking the margin-
al conditional distributions. Further, we assume that:   

ttt yμr  ,  )|( 1 ttt E rμ ,  (14)         

tititiy ,,,  ,  )|var( 1,
2
,  ttiti r ,  (15) 

),,1 ,0(_ ~, iiti tSkewiid  ,  (16) 

where ),,1 ,0(_ tSkew denotes the standardized skewed Student t distribution 

with 2  degrees of freedom, and skewness coefficient 0  (Lambert and 

Laurent 2001). To the marginal return series tir , , d, i ,1  , we fit ARMA-

GARCH models with  skewed Student’s t distributions for the 1-dimensional 
innovations. 

When modeling the joint conditional distribution, the evolution of the con-
ditional copula tC  has to be specified. Usually (Patton, 2004, 2006), the func-
tional form of the conditional copula is fixed, but its parameters evolve through 
time. In this paper, we follow that approach and apply the DCC model proposed 
by Engle (2002), extended to Student’s t copulas. Thus in our DCC-t-copula 
model we assume that the conditional copula tC  is a Student t Copula t

t
C R, such 

that: 

      2121 diagdiag  tttt QQQR ,     (17) 



Małgorzata Doman, Ryszard Doman 78

111  ~~ )1(   tttt QuuQQ  ,    (18) 

where 0 , 0 , 1  , )(~
,

1
, titi utu   , )( ,,, tititi rFu  , d, i ,1  , and 

Q is the unconditional covariance matrix of tu~ . 

2.  The Data 

 In the paper we present results of analysis concerning the dependencies 
between the daily returns for four pairs of indices: S&P500-DAX, S&P500-
WIG20, DAX-WIG20, and DAX-NIKKEI225. We have chosen three indices 
representing stock markets of main economies from different parts of the world. 
The reason for the choice of the WIG20 index is connected with the fact that the 
Polish stock market is significantly influenced by the US financial markets and, 
on the other hand, there exist strong linkages between the Polish and German 
economies.  

 As it was mentioned in Introduction, the very common approach in stock 
market linkages analysis is to investigate the indices of developed markets in 
local currency, and those from emerging markets – denominated in an alterna-
tive currency (mostly in the US dollar). We denominate the considered indices 
in their local currencies, in the USD, and in the euro. Moreover, the dependen-
cies involving the WIG20 are analyzed for the indices denominated in the 
Polish zloty, and those involving the NIKKEI225 – in the Japanese yen. Thus 
our dataset contains the quotations of the considered indices and the exchange 
rates EUR/USD, USD/PLN, EUR/PLN USD/JPY and EUR/JPY. The quotation 
series were obtained from the service Stooq. The period under scrutiny is from 
January 3, 1995 to December 11, 2009.  

Table 1. Descriptive statistics of the analyzed return series 

Index Mean    Maximum Minimum Stand. Dev. Skewness  Kurtosis 
S&P500 0.0238 10.957 -9.4695 1.289 -0.1783 10.9195 

S&P500 in EUR 0.0190 9.5946 -8.7688 1.4663 -0.2152 7.0311 
S&P500 in PLN 0.0282 10.054 -9.1886 1.4320 -0.0718 8.1544 

DAX  0.0276 10.797 -9.791 1.5877 -0.0635 10.9230 
DAX in USD  0.0325 13.5020 -9,4710 1.6741 0.0517 8.5868 
DAX in JPY       
DAX in PLN       

WIG20 0.0302 13.709 -14.161 1.9544 -0.1548 6.7066 
WIG20 in USD 0.0262 14.995 -19.463 2.2717 -0.2531 8.2124 
WIG20 in EUR 0.0212 16.368 -17.481 2.3220 -0.1743 8.6857 

Since the  patterns of non-trading days in national stock markets differ, for 
the purpose of modeling dependencies the dates of observations for each pair of 
indices were checked and observations not corresponding to ones in the other 
index quotation series were removed. The time series under scrutiny are per-
centage logarithmic daily returns calculated by the formula: 



The Impact of the Exchange Rate Dynamics on the Dependencies…   79

)ln(ln 100 ttt PPr  ,  (19) 

where tP  denotes the closing index value on day t .  

The descriptive statistics of the analyzed return series are presented in  
Table 1. In Tables 2–5 we show in-sample estimates of the unconditional corre-
lations. 

Table 2. S&P500 and DAX. Estimates of the unconditional correlation of the returns 

 S&P500 S&P500 in EUR 
DAX 0.5590 0.5309 

DAX in USD  0.5227 ----- 

Table 3. S&P500 and WIG20. Estimates of the unconditional correlation of the returns 

 S&P500 S&P500 in EUR S&P500 in PLN 
WIG20 0.2682 ----- 0.1212 

WIG20 in USD  0.2824 -----  
WIG20 in EUR ----- 0.2749  

Table 4. S&P500 and WIG20. Estimates of the unconditional correlation of the returns 

 DAX DAX  in USD DAX  in PLN 
WIG20 0.4494 ----- 0.3598 

WIG20 in USD  ----- 0.5042  
WIG20 in EUR 0.4887   

Table 5. DAX and NIKKEI225. Estimates of the unconditional correlation of the re-
turns 

 NIKKEI NIKKEI in USD NIKKEI in EUR 
DAX 0.2993 ----- 0.2225 

DAX in USD ----- 0.2616  
DAX in JPY 0,2853   

3.  Empirical Analysis of the Stock Market Linkages 

 The course of presented analysis is as follows. We investigate the depend-
encies between the returns for four pairs of indices: S&P500-DAX, S&P500-
WIG20, DAX-WIG20, DAX-NIKKEI225. In each case we estimate the dynam-
ic copula correlations by means of the DCC-t-copula model described in section 
3. Each pair of indices is considered in a local currency, in the US dollar, and in 
the euro. For S&P500-WIG20 and DAX-WIG20 we additionally take into ac-
count denomination in the Polish zloty, and for DAX-NIKKEI225 – in Japanese 
yen. Moreover, we estimate jointly the dynamic copula correlations for triples 
of returns: S&P500-DAX-EUR/USD, S&P500-WIG20-USD/PLN, DAX-
WIG20-EUR/PLN and DAX-NIKKEI225-EUR/JPY.  

 The advantage of copula models we apply here is that they allow to separate 
the dependence dynamics from the volatility dynamics. The feedback between 
these two features causes many problems in traditional analyses based on multi-



Małgorzata Doman, Ryszard Doman 80

variate volatility models. In our approach the volatility dynamics is captured by 
means of GARCH models and then the dependence structure is modeled. 
It means that  the DCC-t-copula models are estimated using a two-step maxi-
mum likelihood approach. The first step includes fitting a GARCH model to 
each return series (Laurent, 2009). The types of fitted models differ depending 
on currency used to denominate an index (Table 4–5). Next, the GARCH stand-
ardized residuals are transformed by means of their theoretical cumulative dis-
tribution functions to obtain the series of data uniformly distributed on [0,1].  
In the second step the DCC-t-copula models are fitted to the transformed series. 
Thus, we follow the method of inference functions for margins (Joe and Xu, 
1996).  

 The first observation coming from Tables 6–7 is that the conditional mean 
an volatility dynamics is sensitive to denomination. The return series under 
scrutiny are long and include some crisis periods so the fitted GARCH models 
are mostly asymmetric and with a skewed  Student t as an error distribution.  

The DCC-t-copula parameter estimates are presented in Tables 8–11. The re-
sults indicate that the dynamics of dependencies shows a high level of persis-
tence in each considered case. 

Table 6. S&P500 and NIKKEI225. Types of fitted ARMA-GARCH models 

Return  
series 

S&P500 
S&P500 
 in EUR 

S&P500  
in PLN 

NIKKEI225 
 

NIKKEI225 
in USD 

NIKKEI225 
in EUR 

ARMA (1,1) (0,2)  (1,1) (0,0) (0,1) (0,0) 

GARCH 
GJR-

GARCH(1,2) 
GJR-

GARCH(1,2) 
GARCH(1,1) GJR(1,2) GJR(1,2) FIGARCH(1,1) 

Error  
distribution 

Skewed 
Student 

Skewed 
Student 

Skewed 
Student 

Skewed 
Student 

Skewed 
Student 

Skewed 
Student 

Table 7. DAX and WIG20. Types of fitted ARMA-GARCH models 

Return  
series 

DAX 
DAX 

 in USD 
WIG20 

WIG20  
in USD 

WIG20  
in EUR 

ARMA (2,2) (1,0) (0,1) (2,0) (0,0) 
GARCH FIAPARCH(1,1) GARCH(1,1) FIAPARCH(1,1) GJR-GARCH(1,2) FIGARCH(1,1) 

Error  
distribution 

Skewed  
Student 

Skewed  
Student 

Student Student Student 

Table 8. S&P500-DAX. Parameter estimates for the fitted DCC-t-copula model (stand-
ard errors in parentheses) 

 S&P500 and DAX 

Parameter 
in local 

currencies 
in EUR in USD 

S&P500-DAX 
-USD/EUR 

  0.0146 
(0.003 

0.0204 
(0.006) 

0.0185 
(0.003) 

0.0175 
(0.003) 

  0.9841 
(0.004) 

0.9750 
(0.008) 

0.9805 
(0.004) 

0.9789 
(0.004) 

  14.4538 
(3.819) 

13.1894 
(3.582) 

15.5688 
(4.665) 

12.5504 
(1.843) 



The Impact of the Exchange Rate Dynamics on the Dependencies…   81

Table 9. S&P500-WIG20. Parameter estimates for the fitted DCC-t-copula model 
(standard errors in parentheses) 

 S&P500 and WIG20 

Parameter 
in local 

currencies 
in EUR in USD in PLN 

S&P500-WIG20 
-USD/PLN 

  0.0075 
(0.008) 

0.0109 
(0.004) 

0.0102 
(0.004) 

0.0072 
(0.002) 

0.0125 
(0.003) 

  0.9900 
(0.016) 

0.9836 
(0.007) 

0.9878 
(0.005) 

0.9871 
(0.005) 

0.9821 
(0.005) 

  14.6137 
(3.710) 

16.1879 
(4.616) 

14.9618 
(3.911) 

11.3950 
(2.286) 

16.6111 
(3.004) 

Table 10. DAX-WIG20. Parameter estimates for the fitted DCC-t-copula model (stand-
ard errors in parentheses) 

DAX and WIG20 

Parameter 
in local 

currencies 
in EUR in USD in PLN 

DAX-WIG20 
-EUR/PLN 

  0.0125 
(0.005)  

0.0181 
(0.008)  

0.0141 
(0.003)  

0.0109 
(0.003)  

0.0110 
(0.002)  

  0.9875 
(0.007)  

0.9793 
(0.011)  

0.9852 
(0.004)  

0.9865 
(0.003)  

0.9863 
(0.004)  

  12.017 
(2.468)  

12.154 
(2.555)  

14.516 
(3.640)  

14.372 
(3.435)  

17.213 
(3.199)  

Table 11. DAX-NIKKEI225. Parameter estimates for the fitted DCC-t-copula model 
(standard errors in parentheses) 

DAX and NIKKEI225 

Parameter 
in local 

currencies 
in EUR in USD         in JPY 

DAX-NIKKEI 
-EUR/JPY 

  0.0150 
(0.018)  

0.0091 
(0.004)  

0.0080 
(0.003)  

0.0066 
(0.003)  

0.0114 
(0.002)  

  0.9339 
(0.142)  

0.9889 
(0.006)  

0.9900 
(0.004)  

0.9864 
(0.006)  

0.9861 
(0.003)  

  15.029 
(4.870)  

21.162 
(7.524)  

23.087 
(7.556)  

17.4376 
(6.412)  

13.248 
(2.118)  

 Figure 1 shows a comparison of the dynamic copula correlations for the pair 
S&P500-DAX obtained in all the considered cases. The dynamics of the corre-
lations is quite strong. The strongest dependencies are observed in the years 
2001-2004 and 2008-2009. The values of the correlations calculated for the 
indices denominated in local currencies, in the euro, and modeled jointly with 
the exchange rate EUR/USD are quite close each other. Only in the case of  
denomination in the US dollar the correlation estimates are clearly lower. The 
mean levels of the estimated dynamic copula correlations (Table 12) are signifi-
cantly different and the highest mean is obtained in the case of the dependencies 
between the indices and the exchange rate EUR/PLN modeled jointly. The null 
hypothesis about equality of the means was tested using the Model Confidence 



Małgorzata Doman, Ryszard Doman 82

Set (MCS) procedure (Hansen et al., 2003, 2011; Hansen and Lunde, 2007) 
applied to the set of the dynamic copula correlations series.  

 

 
Figure 1. S&P500 and DAX. Dynamic copula correlations from DCC-t-copula model 

 

 
Figure 2. S&P500 and WIG20. Dynamic copula correlations from DCC-t-copula model 

 The estimates of dynamic copula correlations obtained for the pair S&P500-
WIG20 are much lower but show similar pattern as in the previous case – the 
dynamics of the conditional copula correlations is strong but it does not depend 
significantly on the choice of currency. The only exception concerns the clearly 
weaker dependencies in the case of the indices denominated in the Polish zloty.  
The difference is more visible after Poland joining the EU. The testing proce-
dure, the same as in the previous considered case, indicate that the mean levels 

‐0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1 201 401 601 801 1001 1201 1401 1601 1801 2001 2201 2401 2601 2801 3001 3201 3401 3601

in local currencies in EUR

in USD jointly with EURUSD

‐0,2

‐0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

1 201 401 601 801 1001 1201 1401 1601 1801 2001 2201 2401 2601 2801 3001 3201 3401 3601

in local currencies

in USD

in EUR

in PLN

jointly with USDPLN



The Impact of the Exchange Rate Dynamics on the Dependencies…   83

of the estimated dynamic copula correlations (Table 12) are significantly differ-
ent. 

Table 12. Means of the dynamic copula correlation estimates for the pairs S&P500-
DAX and S&P500-WIG20 

S&P500 and  DAX WIG20 
in local currencies 0.4975 0.2434 

in USD  0.4339 0.2345 
in EUR 0.4903 0.2711 

modeled  jointly with the exchange rate 0.4992 0.2455 
in PLN  0.1325 

Table 13. Means of the dynamic copula correlation estimates for the pairs DAX-WIG20 
and DAX-NIKKEI225 

DAX and  WIG20        NIKKEI225 
in local currencies 0.4185 0.2957 

in USD  0.4432 0.2913 
in EUR 0.4436 0.2601 

modeled  jointly with the exchange rate 0.4195 0.3015 
in PLN 0.3386 ------ 
In JPY ------ 0.2571 

 

 
Figure 3. DAX and WIG20. Dynamic copula correlations from DCC-t-copula models 

 The estimates of dynamic copula correlations obtained for the pair DAX-
WIG20 are presented in Figure 3. In general, the differences between the esti-
mates are not very high and the dynamics in all cases is similar. However, once 
again, we can observe the impact of Poland’s EU joining on the conditional 
correlations calculated for the indices denominated in the Polish zloty. Mean 
levels of the conditional correlation estimates are presented in Table 13. The 
testing MCS procedure indicates that the mean levels of the conditional correla-

‐0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1 201 401 601 801 1001 1201 1401 1601 1801 2001 2201 2401 2601 2801 3001 3201 3401 3601

in USD in PLN

jointly with EURPLN in EUR

in local currencies



Małgorzata Doman, Ryszard Doman 84

tions are statistically undistinguishable in the case of denomination in the EUR 
and in the USD and this mean level is the highest one.  

 

 
Figure 4. DAX and NIKKEI225. Dynamic copula correlations from DCC-t-copula 

models 

 The dynamics of the conditional correlations between the returns on the 
DAX and the NIKKEI 225 shows slightly different patterns (Figure 4).  Denom-
inating the indices in the yen results in the lowest values of the correlation esti-
mates. The most interesting thing one can see in Figure 4 is that from the begin-
ning of the financial crisis 2007-2009 the plots of the conditional correlations 
estimates start to disperse. Starting from that point, the dependencies measured 
for the indices denominated in the EUR are the weakest. 

Conclusions 

 The aim of the presented research was to examine how the dynamics of 
linkages between stock markets changes when the exchange rate dynamics is 
introduced into the model. We considered dependencies between the S&P500 
index and two European indices – the  DAX and the WIG20, and for the pairs 
DAX-WIG20 and DAX-NIKKEI225. To analyze the stock indices linkages we 
used DCC-t-copula models. The advantage of the applied approach is that it 
allows to separate the dynamics of linkages from the volatility dynamics.   

 The presented results are slightly ambiguous but generally show that the 
impact of denomination or introducing the exchange rate directly into the model  
for dependencies is rather weak. However, as it was expected, some significant 
changes in the dynamics of the conditional dependence are observed for indices 
denominated in a common currency when events strongly influencing the con-
sidered exchange rates dynamics are present. 

‐0,2

‐0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

1 201 401 601 801 1001 1201 1401 1601 1801 2001 2201 2401 2601 2801 3001 3201 3401

in USD in EUR

in JPY jointly with EURJPY

in local currencies



The Impact of the Exchange Rate Dynamics on the Dependencies…   85

 The question about the proper way of analyzing the dependencies remains 
still open. The problem seems to be less important in the case of  indices de-
nominated in major currencies, i.e. the USD or the EUR, and much more signif-
icant in the case of indices expressed in other (local) currencies.  

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Wpływ dynamiki kursów walutowych                                                       
na zależności na globalnym rynku akcji 

Z a r y s  t r e ś c i. Analiza powiązań pomiędzy narodowymi rynkami akcji jest zwykle oparta na 
modelach opisujących zależności pomiędzy stopami zwrotu z akcji lub indeksów. Przy tym w 
niektórych badaniach wykorzystuje się notowania w walutach lokalnych, a w innych – notowania 
denominowane w tej samej walucie (zwykle w dolarze amerykańskim). W artykule zajmujemy 
się badaniem, jak uwzględnienie dynamiki kursów walutowych w modelu powiązań dla giełdo-
wych stóp zwrotu wpływa na opis zależności. Stosujemy i porównujemy dwa podejścia. Pierwsze 
polega na denominowaniu rozważanych notowań w tej samej walucie, a drugie sprowadza się do 
bezpośredniego wprowadzenia kursu walutowego do modelu struktury zależności. Prezentowana 
analiza jest oparta na szeregach stóp zwrotu z okresu 1995-2010. W celu opisu struktury zależno-
ści stosujemy dynamiczne modele kopuli. Podejście takie pozwala nam na oddzielenie dynamiki 
zależności od dynamiki zmienności notowań. 

S ł o w a  k l u c z o w e: rynek akcji, indeks giełdowy, powiązania, denominacja, kursy waluto-
we, kopula. 


