Volatility Spillovers and Dynamic
Correlation in European Bond Markets
Vasiliki D. Skintzi*
Apostolos-Paul N. Refenes
Financial Engineering Research Center (FRC)
Department of Management Science and Technology
Athens University of Economics and Business
Abstract
This paper examines the volatility transmission mechanism from the US bond
market and the aggregate Euro area bond market to twelve individual European bond
markets. A bivariate EGARCH model with a dynamic conditional correlation
structure that deals with US effects as exogenous is used. Our results suggest that
significant volatility spillovers exist from both the aggregate Euro area bond market
and the US bond market to the individual European markets. Moreover, the price and
volatility spillovers have increased after the European Monetary Union for most
European bond markets.
Keywords: Volatility, spillover, dynamic correlation, Euro
JEL Classification: C32, F30, G15
*
Correspondence author, Financial Engineering Research Centre, Department of Management
Science & Technology, Athens University of Economics and Business, 47A Evelpidon & 33
Lefkados 113 62 Athens, Greece; e-mail: vikiski@aueb.gr
1
1.
Introduction
The liberalization of capital flows facilitated by recent developments in trading
technologies and improved transmission of news has resulted to increased integration
between international financial markets. Understanding the behavior and sources of
international financial markets linkages is important for diversifying internationally,
pricing securities and making asset allocation decisions. The objective of this study is
to investigate the market factors influencing European bond markets. More
specifically, we measure how and to what extent the volatility of a European bond
market is affected by local shocks, regional shocks and world shocks. In addition to
exploring the volatility transmission mechanism, the time-varying correlation
structure between the European bond markets is investigated.
The issue of interdependence among international financial markets has received
significant attention in the finance literature. A number of studies have focused on
stock market interdependence in terms of price and volatility spillovers (e.g. Eun and
Shim, 1989; Hamao, Masulis and Ng, 1990; Koutmos and Booth, 1995). Of particular
interest is the impact of world factors to national stock markets. For example, Bekaert
and Harvey (1997) study the nature of volatility in emerging stock markets and find
that volatility in emerging markets is less influenced by world factors. Ng (2000)
studies the influence of world and regional factors in the Pacific-Basin region. She
finds that both world and regional factors influence the Pacific-Basin stock markets
although the influence of world factors is more intense.
This study focuses on the magnitude and the changing nature of price and
volatility spillovers in the European bond markets. The recent developments within
the European Monetary Union (EMU) have resulted to increased stock market
interdependence among EMU countries and, consequently, question the dominance of
the world financial markets in the Euro area. Fratzscher (2002) investigates shock
spillovers from US to European equity markets. He finds that the transmission of
shocks from the Euro area has become more important compared to shocks from the
US market. The aim of our study is to investigate how local, regional and world
market factors affect the European bond markets by measuring how and to what
extent the volatility of a European market is affected by shocks in the same country,
in the aggregate Euro area bond market and, finally, outside Europe (US).
2
The contribution of this study is threefold. While most of the previous studies
have focused on the interaction between a single pair of countries, we investigate the
influence of two major market factors, regional and world, to both Euro and non Euro
area national bond markets within the European region. Secondly, this study focuses
on the relationships between bond markets that, relative to equity markets, are less
studied in the literature (see Clare and Lekkos, 2000). Thirdly, most approaches for
modeling volatility spillovers assume conditional time-invariant correlations in order
to simplify the estimation procedure (see Booth et al, 1997; Laopodis, 2002;
Miyakoshi, 2002). However, several studies (e.g. Erb et al, 1994, and Longin and
Solnik, 1995, amongst others] provide evidence that support the time-variability of
correlation. This study builds upon the methodology developed by Darbar and Deb
(2002) and models volatility spillovers assuming a time-varying conditional
correlation. Finally, extending the sample period beyond the launch of Euro in
January 1999, allows us to test how the bond markets interdependence has changed
after this major event.
The volatility transmission mechanism is modeled using a multivariate extension
of
Nelson’s
(1991)
Exponential
General
Autoregressive
Conditional
Heteroscedasticity (EGARCH) model. The model used allows for both mean and
volatility spillovers and captures potential asymmetries in the volatility spillover
mechanism. Similar approaches for modeling volatility spillovers have been used in
Kootmos and Booth (1995), Booth et al (1997), Ng (2000), So (2001). Moreover, the
multivariate model allows for a dynamic structure of conditional correlation.
The overall results indicate that there are short-run dynamic relationships between
the individual European bond markets and the aggregate Euro area bond market in
terms of both price and volatility spillovers. The price and volatility spillover process
as well as the correlation structure has significantly changed for a number of
European bond markets after the introduction of Euro. Finally, the US bond market
significantly influences the individual European bond markets in terms of both price
and volatility spillovers.
The remainder of this paper is organized as follows. Section 2 presents the
bivariate EGARCH model used for modeling volatility spillovers and the dynamic
correlation structure. Section 3 describes the dataset and reports some preliminary
3
statistics. Section 4 presents and analyses the empirical results, and Section 5
concludes.
2.
Volatility Spillover Model
The aim of this analysis is to investigate the sources of volatility for bond markets
in the European region. Bekaert and Harvey (1997) construct a volatility spillover
model by assuming two sources of volatility, local and world factors. Ng (2000)
extends her model assuming stock markets are affected by three sources of shocks,
local, regional and world. Miyakoshi (2003) uses a bivariate EGARCH model
between local stock market and regional factors and models world shocks as
exogenous factors for the case of Asian equity markets. Our empirical volatility
spillover model is based upon the models developed in these studies. More
specifically, the volatility spillover mechanism in a European bond market is modeled
by assuming three sources of shocks, local, regional and world. Regional shocks are
represented by the returns of an aggregate Euro area bond market index, while world
shocks are represented by the returns in the US bond market. Following Miyakoshi
(2003), regional shocks are modeled as an endogenous variable, while shocks in the
US bond market are an exogenous variable in the bivariate volatility spillover model
between Euro area index and each European bond market.
A well documented empirical finding in the finance literature is that bad news
have a larger impact on volatility than good news. However, while this empirical
finding has been widely explored for stock markets (see Koutmos and Booth, 1995,
and Booth et al, 1997, amongst others), the asymmetric phenomenon in bond returns
volatility has received little attention. To capture the potential asymmetric behavior of
bond returns and avoid imposing non-negativity constraints on GARCH parameters,
we employ a multivariate version of the EGARCH model developed by Nelson
(1991).
Suppose Ri,t, REU,t and RUS,t represent the weekly return of a European market i,
the Euro area index, and US, respectively, at time t. Ωt-1 is the information set
2
available at time t-1.  i2,t ,  EU
,t , and σEUI,t are the conditional variances of the
European market i and the Euro-area regional index, and the conditional covariance
between the European market and the Euro area index, respectively. εi,t and εEU,t are
4
the innovations of bond market i and the aggregate Euro area index, while zi,t and zEU,t
are the standardized innovations, i.e. zi,t =  it /  i ,t . An EGARCH model for each
European bond market i (i = 1,…,N) including both price and volatility spillovers is
formulated as follows:
 Ri ,t   i 0    i1



 REU ,t    EU 0    EU 1
i 2   Ri ,t 1   i RUS ,t 1    i ,t 




 EU 2   REU ,t 1   EU RUS ,t 1    EU ,t 
  i ,t 
εi ,t It 1  

  EU ,t 
  i2,t
H i ,t  

 iEU ,t
(1)
N  0, H i ,t 
(2)
 iEU ,t 

2
 EU
,t 
(3)
2
ln  i2,t    i 0   ii fi  zi ,t 1    iEU f EU  zEU ,t 1    i ln  i2,t 1   i ln  RUS
,t 1 
(4)
2
2
2
ln  EU
,t    EU 0   EUEU f EU  z EU ,t 1    EUi f i  zi ,t 1    EU ln  EU ,t 1    EU ln  RUS ,t 1  (5)


fi  zi ,t 1   zi ,t 1  E zi ,t 1   i zi ,t 1
 
(6)
where E z i ,t   2 /  
1/ 2
The conditional mean equation is specified in equation (1), and the parameters βi2
and βEU1 measure the impact of the Euro area aggregate bond market returns on the
returns of bond market i and the impact of the returns of bond market i on the Euro
area index returns, respectively. Also, λi and λEU measure the impact of US market
returns on the European market i and the Euro area market returns, respectively. The
conditional variance equation of bond market i, described in equation (4), contains a
function of lagged standardized residuals from the Euro area index and its own lagged
residuals. The parameter αiEU is the volatility spillover coefficient, while parameter γi
measures the degree of volatility persistence.
5
Asymmetry in the volatility process is modeled by equation (6). Parameter δi
measures the asymmetric impact of innovations, with the partial derivatives being:
1   i , for zi  0
fi  zi ,t  / zi ,t  
-1+ i , for zi  0
(7)
  in equation (6) measures the size effect, while the term δ z
The term zi ,t  E zi ,t
i i,t
measures the sign effect. If δi is negative, a negative innovation tends to reinforce the
size effect, while a positive innovation tends to partially offset it. Thus, a significant
and negative δi coefficient provides evidence of asymmetry. The relative importance
of negative innovations to positive innovations in the volatility process is measured by
the ratio, 1   i / 1   i  . Finally, the impact of US squared market returns in the
individual local markets and the Euro area regional market is reflected in coefficients
φi and φEU.
To take into account the time-variability of conditional correlation, we employ a
methodology developed by Darbar and Deb (2002). The conditional covariance σiEU,t
is modeled as a function of the conditional correlation and variances. In order to
ensure that the conditional correlation ρiEU,t falls into the range (-1,1), an index
function ξiEU,t  (-,) is used. The correlation index function is assumed to depend
on the cross-products of the standardized innovations and the past values of the index
function. The conditional correlation is a logistic transformation of the index function.
 iEU ,t  iEU ,t i ,t EU ,t

1

 1  exp  ij ,t  


(8)

iEU ,t  2 
iEU ,t  c0i  ciEU zi ,t 1 z EU ,t 1  giEU iEU ,t
(9)
(10)
A number of studies e.g. Fratzscher (2002), Billio and Pelizzon (2003) have
documented that links between stock markets have changed before and after EMU. In
6
order to account for possible change in the spillover parameters, dummy variables are
added in the spillover parameters as well as in the correlation index function as
follows:
 i 2,t   i 2   i*2 Dt ,
*
 EU 1,t   EU 1   EU
1 Dt
i ,t  i  i* Dt ,
*
EU ,t  EU  EU
Dt
*
*
 iEU ,t   iEU   iEU
Dt ,  EUi ,t   EUi   EUi
Dt
i ,t  i  i* Dt ,
(11)
*
 EU ,t   EU   EU
Dt
c0i ,t  c0i  c0*i Dt
Given a sample of T observations the parameters of the bivariate EGARCH model
are estimated by maximizing the log-likelihood function:
T
L  θ    lt  θ   T ln 2 
t 1
1 T
1 T '
ln
H
θ



 t
 ε  θ  H t1εt θ 
2 t 1
2 t 1 t
(12)
where θ is the parameter vector of the model. The algorithm developed by Berndt et
al (1974) is used to maximize the log likelihood function and obtain parameters
estimates via Quasi Maximum Likelihood estimation. Statistical inference is based on
robust test statistics developed by Bollerslev and Wooldridge (1992) to take into
consideration the non-normality of residuals.
3.
Data description and preliminary statistics
Data employed in this study consist of weekly bond total return indices from eight
Euro area countries (Austria, Belgium, France, Germany, Ireland, Italy, Netherlands,
Spain), four non Euro area countries (Denmark, Norway, Sweden, UK) and the US.
The choice of such a broad sample enables us to compare the volatility spillover
mechanism between countries that have or have not joined the Euro. The data are
sampled weekly (Friday-to-Friday) over the period from 1 February 1991 to 31
December 2002. Datastream Benchmark Bond Indices with five years average
7
maturity are used as proxies of the bond markets. We use Datastream indices, as they
are broader measures of market returns and tend to be more homogenous. Returns are
calculated as the growth rate of the bond indices, Rit = log(Pt/Pt-1), measured in terms
of US dollars 1 . Weekly returns are used in order to avoid the problem of nonsynchronous trading and the day-of-the-week effects.
The euro area index return is calculated for each Euro area bond market as a
weighted-average of the markets that have joined the Euro excluding the market under
consideration. For each individual bond market i, it is calculated as follows:
N
REU ,t 
w
Rk ,t
k ,t
k i
N
w
k i
(13)
k ,t
where k includes only the countries that have joined the euro, and wk,t is the share of
the market capitalization of bond market k in the total Euro area bond market. In the
case of the non Euro area bond markets, the Euro area index is the market value
weighted index of the eight Euro area bond markets in the sample.
Summary statistics for the weekly returns of the twelve European bond markets,
as well as for the US bond market are presented in Table 1. The average weekly
returns in the European bond markets range from 0.138% (in Germany) to 0.211% (in
Italy), while the standard deviations range from 0.004 to 0.007. The skewness and
excess kurtosis statistics indicate that negative shocks are more common than positive
shocks, while large shocks are more frequent than expected in all bond markets.
Moreover, all returns series are not normal. This is also confirmed by the Jarque-Bera
statistic that rejects the null hypothesis of zero skewness and excess kurtosis for all
European bond markets in the sample at the 5% significance level. Among the
European and US bond markets, the first-order autocorrelation ranges from -0.102 to
0.051 and the Ljung-Box statistic indicates the persistence of linear dependence up to
seven lags in Belgium, Netherlands, Norway, Sweden and US. The Ljung-Box
1
Weekly index closing prices are measured in a common currency, following Ng (2000), Billio and
Pelizzon (2003). The underlying assumption is that investors are unhedged against foreign exchange
risk.
8
statistic for the squared returns shows evidence of non-linear dependence in all
markets (except from Germany and Netherlands). Moreover, applications of the
ARCH Lagrange Multiplier (LM) test of Engle (1980) provide evidence for the
existence of ARCH effects in the European and US bond markets.
To obtain an idea for the extent of linkages between European bond markets and
US, Table 2 presents the unconditional contemporaneous correlations between the
Euro area / US and European bond markets. For the whole sample period the
correlations between the individual European markets and the Euro area range from
0.619 to 0.840, while the correlations between the European markets and US range
from 0.189 to 0.476. To further investigate whether the bond market linkages have
changed over time, the sample period was divided into two sub-periods before and
after the introduction of Euro (1 January 1999). In all pairs, the intertemporal
dependencies have strengthened after the introduction of Euro. This suggests that the
globalization of the bond markets has substantially increased as a result of the EMU.
4.
Empirical Results
4.1 Volatility Spillover Effects
The objective of this study is to investigate the spillover mechanism between
European bond markets including the effects of the US bond market as an exogenous
variable. The bivariate EGARCH model applied in the analysis allows for both price
and volatility spillover as well as for time-varying correlation structure. To evaluate
the appropriateness of the estimated spillover model, the Ljung-Box test for the 24th
order serial correlation in the level and squared standardized residuals as well as the
Engle and Ng (1993) asymmetric tests are performed. Table 3 depicts the p-values of
the residual diagnostic tests. The Ljung-Box test statistics provide no evidence of
linear or non-linear dependence in the standardized residuals. Moreover, with the only
exception of Italy, no linear dependence is found in the cross product of standardized
residuals indicating that the model correlation structure is not misspecified. The
asymmetric test statistics depict that the bivariate EGARCH model captures the
interaction between the bond markets adequately with the exception of the positive
sign bias test for Belgium and France.
9
The maximum likelihood estimates of the bivariate EGARCH model for the Euro
area and non Euro area bond markets are reported in Tables 4 and 5, respectively.
Price spillovers from the aggregate Euro area bond market to the individuals
European bond markets and vice-versa are measured by coefficients βiEU and βEUi,
respectively. For the case of Euro area bond markets, the estimated coefficients
provide evidence of significant price spillovers from the aggregate Euro area bond
market to Belgium, France, Netherlands, and Spain. From these bond markets only
Belgium and France exhibit reciprocal spillovers to and from the aggregate Euro area
bond market. No linear dependencies in either way exist for the rest Euro area and the
four non Euro area bond markets.
Turning to second moment interdependencies, volatility spillovers, measured by
coefficients αiEU and αEUi, are more extensive and reciprocal. Significant two-way
volatility spillovers exist in Belgium, France, Germany, and Italy from and to the
Euro area aggregate bond market index. Additionally, the Euro area index volatility
spills to Austria and Spain. Netherlands is the only bond market within the Euro area
that volatility spills to the aggregate Euro area bond market, while no significant
spillovers exist for the Euro area index to this market. For the non Euro area bond
markets, significant reciprocal volatility spillovers exist for Denmark and UK bond
markets to and from the aggregate Euro area bond market index. Additionally,
Norway volatility spills to the Euro area index, while the Euro area index volatility
spills to Sweden.
The volatility persistence in the European bond markets volatility process implied
in equation (4) is measured by the coefficient γi. The values of γi coefficients in Tables
5 and 6 provide evidence of strong volatility persistence in all countries. The
estimated coefficients are significant and close to one for all countries. Austria
exhibits the strongest persistence, while UK exhibits the weakest persistence.
Moreover, the own market effects measured by coefficients βi1 and αii are significant
in the price and volatility process of most European bond markets.
The price and conditional variance processes specified in equations (1) - (6)
permit own market shocks and shocks in the Euro area bond index to have an
asymmetric impact in the volatility process of each European bond market and vice
versa. Economically speaking, this means that negative innovations in one market
have greater impact in the volatility process of the other market than positive
10
innovations. Our results indicate that shocks in the aggregate Euro area bond index
have an asymmetric impact in the bond market volatility process of Austria, Belgium,
France, Italy and the four non Euro area markets.
Turning to the US exogenous effects, bond market returns for Austria, Belgium
Spain, Denmark, Norway and Sweden are significantly influenced by the world factor
of the US bond market. In all Euro area bond markets, volatility is significantly
affected by the US bond market volatility. In the case of the non Euro area markets,
bond market volatility is not influenced by the US market volatility with the exception
of Norway. Interestingly, in all cases the following equations hold:
iEU  i ,
ii  i
(14)
The results of equation (14) suggest that European bond market volatilities are more
influenced by the regional Euro area factor than by the US factor supporting the
exogeneity of the US market. Additionally, the own market volatility effects have a
stronger impact in the individual European bond market volatility that the exogenous
US volatility effects.
By including the Euro dummy variables described in equation (11) we allow the
price and volatility spillover parameters to take different values before and after the
introduction of Euro. The estimated coefficients for the dummy variables indicate that
the price spillovers from the Euro area index to the individual Euro area bond markets
have significantly increased after the introduction of Euro with the only exception of
Ireland. Turning to the volatility processes, the volatility spillover parameters from the
aggregate Euro area bond index to Germany, Italy and Sweden and the volatility
spillovers from Belgium, France, Germany, Italy, Netherlands and Denmark to the
aggregate Euro area bond market have increased after the introduction of Euro. The
exogenous effect of US to the European bond market returns has not been affected by
the introduction of Euro.
The specification of our model is based on the assumption of exogeneity of the US
market and endogeneity of the Euro area market index. We test this specification by
treating the US bond market as endogenous and the aggregate Euro area bond market
index as exogenous in the volatility spillover model. Table 6 presents the results for
11
the price and volatility spillovers from US to the individual European bond markets
(coefficients βi2, and αiUS) and from the individual European bond markets to US
(coefficients βUS1 and αUSi). While price and volatility spillovers from US to several
European bond markets are significant, almost none of the individual European bond
markets affect the US bond market returns and return volatility. More specifically,
only the German bond market returns and the UK bond market volatility significantly
affect the US bond market return and volatility, respectively.
4.2 Time-varying conditional correlations
Similar to the parameters obtained usually from the estimation of the conditional
variance process, the ARCH parameters ciEU in the conditional correlation equation
are generally small and significant. The GARCH parameters giEU are large and close
to one indicating that time-varying correlation exhibits a high degree of persistence.
These results are similar to the parameter estimation of the conditional correlation
equations estimated in Darbar and Deb (2002). With the inclusion of an additive
dummy variable in the conditional correlation equation described in equations (8) (10), we conclude that the correlation between the individual European bond market
and the aggregate Euro area bond market has increased after the introduction of Euro
in the case of Germany, Italy, Netherlands and Denmark. Only the correlation
between Belgium and the Euro area bond market has significantly decreased after the
introduction of Euro.
The estimated conditional correlations from the bivariate EGARCH model
between each one of the Euro area bond markets and the aggregate Euro area bond
index are displayed in Figure 1. In all cases bond market return correlations exhibit a
significant variation and have a number of spikes. Apparently, there is a significant
increase in correlation levels after January 1999. Additionally, the variation of
conditional correlations reduces significantly after the introduction of Euro. Figure 2
presents the estimated conditional correlations between each of the four non Euro area
bond markets and the Euro area bond market index. Apparently, the correlation
structure does not change significantly before and after the introduction of Euro with
the exception of Denmark. The lowest levels of correlation are exhibited between the
UK bond market return and the aggregate Euro area bond market returns.
12
5.
Conclusions
This paper investigates the magnitude and changing nature of the volatility
spillovers from the aggregate Euro area bond market and the US bond market to
eleven individual European bond markets. The econometric methodology used to
model the volatility transmission mechanism allows us to investigate the price and
volatility transmission mechanism as well as the time-varying correlation structure
between the individual European bond markets and the aggregate Euro area bond
market index.
The empirical results of this study are threefold. Firstly, significant price and
volatility spillovers exist between the aggregate Euro area bond market and the
individual European bond markets both within and outside the Euro area. The second
moment interdependencies are far more pronounced and reciprocal than the first
moment interdependencies. Moreover, the own market effects are significant in the
price and volatility process of most European bond markets. In most of these markets
local and regional shocks have an asymmetric impact in the bond market volatility
process. While this is a well-documented stylized fact for stock market returns, it has
not been extensively investigated for bond market returns.
Secondly, the results of our analysis indicate that the world market factor of US
has a significant influence in the individual European bond market volatility process.
While the US market returns influence the European bond market returns in a limited
number of cases, the US bond market volatility is a significant factor in explaining the
individual European bond market volatilities in almost all cases. Finally, the
introduction of Euro has significantly affected the price and volatility transmission
mechanism in both Euro area and non Euro area bond markets. In most European
bond markets, the price and volatility spillover coefficients from and to the aggregate
Euro area index have significantly increased after this major event. Furthermore, the
correlation levels among the European countries have increased and become more
stable after the introduction of Euro.
13
References
Bekaert, G., Harvey, C.R., 1997. Emerging equity market volatility. Journal of
Financial Economics 43, 29-77.
Berndt, E., Hall, B., Hall, R., Hausman, J., 1974. Estimation and inference in
nonlinear structural models. Annals of Economics and Social Measurement 3,
653-665.
Billio, M., Pelizzon, L., 2003. Volatility and shocks spillover before and after EMU in
European stock markets. Journal of Multinational Financial Management 13, 323340.
Bollerslev, T., Wooldridge, J., 1992. Quasi-maximum likelihood estimation and
inference in dynamic models with time-varying covariances. Econometric
Reviews 11, pp. 143-172.
Booth, G.G., Martikainen, T., Tse, Y., 1997. Price and volatility spillovers in
Scandinavian stock markets. Journal of Banking and Finance 21, 811-823.
Clare, A., Lekkos, I., 2000. An analysis of the relationships between national bond
markets. Bank of England Working Paper Series No 123.
Darbar, S.M., and Deb, P., 2002. Cross-market correlations and transmission of
information. Journal of Futures Markets 22, pp. 1059-1082.
Engle, R.F., 1980. Autoregressive conditional heteroscedasticity with estimates of the
variance of U.K. inflation. Econometrica 50, 987-1008.
Engle, R.F., Ng, V.K., 1993. Measuring and testing the impact of news on volatility.
Journal of Finance 48, 1749-1778.
Erb, C.B., Harvey, C.R., & Viskanta, E., 1994. Forecasting international equity
correlations. Financial Analysts Journal, 6, 32-45.
Eun, C.S., Shim, S., 1989. International transmission of stock market movements.
Journal of Financial and Quantitative Analysis 24, 241-256.
Hamao, Y., Masulis, R.W., Ng, V.K., 1990. Correlations in price changes and
volatility across international stock markets. Review of Financial Studies 3, 281307.
Fratzscher, M., 2002. Financial market integration in Europe: On the Effects of EMU
on Stock Markets. International Journal of Finance and Economics 7, 165-193.
14
Koutmos, G., Booth, G.G., 1995. Asymmetric volatility transmission in international
stock markets. Journal of International Money and Finance 14, 747-762.
Laopodis, N., 2002. Volatility linkages among interest rates: Implications for
monetary policy. International Journal of Finance and Economics 7, 215-233.
Longin, F., & Solnik, B., 1995. Is correlation in international equity markets constant?
Journal of International Money and Finance, 14, 3-26.
Miyakoshi, T., 2003. Spillovers of stock return volatility to Asian equity markets from
Japan and the US. International Financial Markets, Institutions & Money 13, 383399.
Nelson, D.B., 1991. Conditional heteroscedasticity in asset returns: a new approach.
Econometrica 59, 347-370.
Ng, A., 2000, Volatility spillover effects from Japan and the US to the Pacific Basin.
Journal of International Money and Finance 19, 207-233.
So, R.W., 2001. Price and volatility spillovers between interest rates and exchange
value of the US dollar. Global Finance Journal 12, 95-107.
15
TABLES
Table 1
Summary statistics for weekly returns in European bond markets and US
Country Mean (%) Std. Dev.
ρ(1)
LB(7)
ρ2(1)
LB2(7)
-0.024
-0.047
-0.027
-0.033
0.020
0.039
0.036
0.022
9.879
18.703 *
11.965
13.467
12.510
6.772
16.923 *
8.430
0.047
0.131
0.028
0.007
0.058
0.107
0.000
0.097
34.656 *
47.901 *
34.386 *
11.684
30.748 *
63.477 *
4.127
109.020 *
36.105 *
37.817 *
25.721 *
9.917
28.318 *
40.957 *
3.417
106.870 *
0.048
0.051
-0.102
-0.014
-0.067
12.148
22.110 *
22.142 *
12.649
19.276 *
0.087
0.045
0.081
0.195
0.005
36.145
66.748 *
29.601
84.327
16.352 *
24.101 *
40.115 *
28.836 *
77.987 *
16.251
ARCH LM(7) Skewness
Kurtosis
JB statistic
-0.438 *
-0.233 *
-0.138
-0.328 *
0.201 *
-0.127
-0.220 *
-0.138 *
4.429 *
5.327 *
4.423 *
4.517 *
9.258 *
6.651 *
6.023 *
9.991 *
72.573 *
145.556 *
54.297 *
70.559 *
1015.758 *
346.632 *
241.014 *
1264.709 *
-0.692 *
-0.349 *
0.191 *
0.308 *
-0.300 *
9.257 *
7.407 *
10.085 *
6.815 *
3.964 *
1060.718 *
514.263 *
1300.371 *
385.724 *
33.386 *
Euro area markets
AUS
BEL
FRA
GER
IRE
ITA
NETH
SPA
0.144
0.153
0.145
0.138
0.166
0.211
0.144
0.196
0.004
0.005
0.005
0.004
0.006
0.007
0.004
0.007
Non Euro area markets
DEN
NOR
SWE
UK
US
0.160
0.159
0.182
0.163
0.141
0.006
0.005
0.007
0.006
0.006
* denotes significance at the 5% level of confidence
16
Table 2
Unconditional contemporaneous correlations among bond markets
Full Sample
1/2/91-31/12/98
1/1/99 – 31/12/02
Euro Area markets
Country
AUS
BEL
FRA
GER
IRE
ITA
NETH
SPA
With Euro
area
0.763
0.804
0.836
0.811
0.732
0.619
0.840
0.689
With US
With US
0.366
0.398
0.458
0.438
0.444
0.257
0.476
0.189
With Euro
area
0.732
0.736
0.782
0.744
0.660
0.542
0.778
0.630
With US
0.270
0.273
0.340
0.321
0.356
0.159
0.366
0.062
With Euro
area
0.828
0.964
0.956
0.948
0.928
0.969
0.963
0.945
0.302
0.268
0.278
0.451
0.747
0.653
0.604
0.611
0.194
0.183
0.189
0.385
0.921
0.702
0.823
0.795
0.588
0.470
0.590
0.640
0.512
0.672
0.706
0.688
0.678
0.644
0.698
0.621
Non Euro area markets
DEN
NOR
SWE
UK
0.790
0.668
0.646
0.659
Table 3
Diagnostic Checking: P values of test statistics
Ljung-Box Q(24) statistic
Country LB(24)
AUS
BEL
FRA
GER
IRE
ITA
NETH
SPA
DEN
NOR
SWE
UK
0.8190
0.2240
0.5390
0.4920
0.6460
0.7170
0.5440
0.5540
0.2760
0.5360
0.9340
0.2420
LB2(24) LB12(24)
0.2960
0.1370
0.6200
0.3270
0.3200
0.1730
0.4520
0.8470
0.2130
0.5260
0.9050
0.3400
0.5300
0.5040
0.4450
0.6050
0.2450
0.0000
0.6170
0.8870
0.1910
0.4510
0.8520
0.6330
Engle and Ng (1993) diagnostics tests
Sign bias Negative size Positive size
Joint test
test
bias test
bias test
0.9132
0.2856
0.2324
0.2011
0.3180
0.7381
0.0229
0.0536
0.0776
0.7929
0.0203
0.0732
0.6130
0.3471
0.4125
0.3148
0.3037
0.9857
0.8950
0.4912
0.2824
0.1915
0.5982
0.6039
0.7477
0.4431
0.4929
0.5325
0.1771
0.3052
0.1806
0.5300
0.5112
0.7719
0.5009
0.4640
0.4078
0.7625
0.2384
0.1052
0.0520
0.7443
0.0495
0.1073
0.4279
0.8599
0.9077
0.6496
17
Table 4
Results of the bivariate EGARCH models for the Euro area bond markets
AUS
BEL
FRA
Price spillover parameters
βi2
-0.030 0.221** -0.337**
βi2*
0.238** 0.273** 0.224**
βEU1
0.041 -0.347** 0.362**
βEU1*
0.219** 0.267** 0.205**
Variance spillover parameters
αiEU
0.152** 0.464** 0.380**
αiEU*
0.029
0.022
0.017
αEUi
0.041 -0.153** -0.114**
αEUi*
-0.004
0.012
0.002
Own effects
βi1
0.001
0.001 0.003**
αii
0.126** 0.340** 0.079
USA effects
λi
0.252** 0.189** 0.103
λi*
-0.009
-0.064
0.290
φi
0.014** 0.038** 0.020**
φi*
0.000
0.001
-0.002
Volatility persistence
γi
0.995** 0.985** 0.980**
Asymmetry
δi
3.837 -0.762** -1.922**
δEU
-0.734** -0.219** -0.349**
Correlation index parameters
c0i*
-0.003 -0.036**
0.005
ciEU
0.084** 0.086** 0.071**
giEU
0.996** 1.005** 1.001**
GER
IRE
ITA
NETH
SPA
-0.190
0.348**
0.113
0.305**
0.138
0.053
-0.061
0.094
0.127
0.148**
0.012
0.157**
-0.307**
0.331**
0.171
0.284**
-0.015**
0.254**
0.020
0.273**
0.093**
0.130**
0.083**
0.116
0.138
0.053
-0.061
0.094
-0.141**
0.149**
0.198**
0.105**
0.059
0.010
0.095**
-0.009
0.234**
-0.010
0.049
-0.089**
0.001**
0.159**
0.001**
0.180**
0.002**
0.353**
0.001**
0.219**
0.002**
0.050
0.170
-0.101
0.022**
-0.001
0.154
0.115
0.021**
0.000
0.152
-0.163
0.043**
0.001
0.132
-0.108
0.023**
-0.001
0.290**
-0.113
0.016**
-0.001
0.990**
0.993**
0.981**
0.994**
0.983**
0.118
0.110
0.010
0.069
-0.220**
-0.245**
1.327
-1.716
-0.021
0.165**
0.080**
0.108**
0.977**
0.061 0.202**
0.088** 0.130**
0.982** 0.955**
0.053**
0.031
0.087** 0.120**
0.987** 0.989**
** denotes significance at the 5% level of confidence. t-statistics are calculated using
Bollerslev and Wooldridge (1992) robust standard errors.
18
Table 5
Results of the bivariate EGARCH model for the non Euro area bond markets
DEN
NOR
SWE
Price spillover parameters
βi2
0.050
0.024
0.000
βi2*
0.013 0.158** 0.200**
βEU1
0.028
-0.113
-0.035
βEU1*
0.004 0.146** 0.138**
Variance spillover parameters
αiEU
0.261** -0.015 0.111**
αiEU*
0.107
-0.073 0.213**
αEUi
-0.114** 0.305**
0.064
αEUi*
0.100** -0.019
-0.070
Own effects
βi1
0.000
0.001
0.001
αii
-0.210** -0.677** -0.155
USA effects
λi
0.253** 0.200** 0.291**
λi*
-0.095
0.050
-0.233
φi
-0.004 -0.012** -0.006
φi*
0.002
-0.001
0.000
Volatility persistence
γi
0.980** 0.937** 0.989**
Asymmetry
δi
-0.420** -0.192
-0.314
δEU
-0.337** -1.440** 0.194**
Correlation index parameters
c0i*
0.135**
0.028
0.015
ciEU
0.043** 0.109** 0.093**
giEU
0.944** 0.958** 0.953**
UK
0.051
0.025
0.051
-0.096
0.182**
0.029
0.153**
-0.130
0.001**
-1.061**
0.124
-0.039
-0.012
0.004
0.893**
0.400
-0.512**
0.006
0.024
0.970**
** denotes significance at the 5% level of confidence. t-statistics are calculated using
Bollerslev and Wooldridge (1992) robust standard errors.
19
Table 6
The exogeneity of the US market
Return Equation
βi2
βUS1
Euro area markets
AUS
0.255**
0.075
(2.654)
(1.396
BEL
0.194
-0.028
(1.777)
(-0.538
FRA
0.205**
0.016
(2.088)
(0.260
GER
0.258**
0.108**
(2.666)
(2.090)
IRE
0.164
0.006
(1.712)
(0.153)
ITA
0.191
-0.021
(1.621)
(-0.969)
NETH
0.195
0.104
(1.958)
(1.912)
SPA
0.368**
0.035
(3.004)
(0.919)
Non Euro area markets
DEN
0.258**
0.097
(2.715)
(1.606)
NOR
0.175
0.036
(1.774)
(1.287)
SWE
0.168
-0.015
(1.459)
(-0.682)
UK
0.078
-0.018
(0.968)
(-0.684)
Variance Equation
αiUS
αUSi
-0.047
(-1.233)
0.021
(0.452)
-0.096
(-1.655)
-0.021
(-0.433)
-0.094**
(-2.266)
0.066
(1.146)
-0.025
(-0.528)
-0.057
(-0.880)
0.107
(1.559)
-0.055
(-1.726)
0.084
(1.262)
0.068
(1.127)
-0.078
(-2.013)
-0.045
(-1.622)
0.080
(1.280)
-0.039
(-1.161)
-0.048**
(-2.034)
-0.066**
(-2.068)
-0.029
(-1.182)
-0.078**
(-3.470)
-0.040
(-1.316)
-0.035
(-1.160)
-0.001
(-0.020)
-0.085**
(-2.395)
20
FIGURES
Austria
1
0.95
0.9
0.85
0.8
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Belgium
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
France
1
0.95
0.9
0.85
0.8
0.75
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Germany
1
0.95
0.9
0.85
0.8
0.75
0.7
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Fig. 1.Estimated conditional correlations between the Euro area bond markets and the aggregate Euro area index.
21
Ireland
1
0.9
0.8
0.7
0.6
0.5
0.4
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Italy
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Netherlands
1
0.95
0.9
0.85
0.8
0.75
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Spain
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Fig. 1. (continued)
22
Denmark
1
0.98
0.96
0.94
0.92
0.9
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Norway
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Sweden
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
UK
0.85
0.8
0.75
0.7
0.65
0.6
0.55
Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02
Fig. 2.
Estimated conditional correlations between non Euro area bond markets and the aggregate Euro area
index.
23