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The spread of the global financial crisis of 2008/2009 was rapid, and impacted the functioning and the performance of financial markets. Due to the importance of this phenomenon, this study aims to explain the impact of the crisis on stock market behavior and interdependence through the study of the intraday volatility transmission. This paper investigates the patterns of linkage dynamics among three European stock markets—France, Germany, and the UK—during the global financial crisis, by analyzing the intraday dynamics of linkages among these markets during both calm and turmoil phases. We apply a VAR-EGARCH (Vector Autoregressive Exponential General Autoregressive Conditional Heteroscedasticity) framework to high frequency five-minute intraday returns on selected representative stock indices. We find evidence that interrelationship among European markets increased substantially during the period of crisis, pointing to an amplification of spillovers. In addition, during this period, French and UK markets herded around German market, possibly explained by behavior factors influencing the stock markets on or near dates of extreme events. Germany was identified as the hub of financial and economic activity in Europe during the period of study. These findings have important implications for both policymakers and investors by contributing to better understanding the transmission of financial shocks in Europe.

The recent global financial crisis has considerably affected financial markets and is considered the most devastating crisis since the Great Depression of 1929. According to data from the World Federation of Exchanges, at the end of 2007 the world equity market capitalization was more than $64 trillion and sharply declined in 2009 to stand at $49 trillion—a drop of 22%, which is equal to 25% of global GDP for 2009. This crisis, which mainly originated in the US market, spread rapidly and dangerously to developed and emerging financial markets and to real economy around the world. A study by Bartram and Bodnar [

This paper contributes to these ongoing debates by investigating the interrelationship between financial markets and their market behavior changes during financial turmoil, especially during periods of high risk. Studying market interrelationship will provide evidence of their market behavior, whereas pointing out sudden changes in cross-market linkages after a shock affecting markets will allow better investigation of the phenomenon of contagion during financial crises. A better understanding of these issues has become the key to portfolio allocation and risk management activities, and therefore central for investors, academics and policymakers.

In our analysis, we adopt the definition of Forbes and Rigobon [

Since the provocative paper by Forbes and Rogobon [

Using more advanced techniques, such as a multivariate regime-switching copula model, Kenourgios

Syllignakis and Kouretas [

A second approach of studying cross-market linkages is based on testing for changes in the cointegrating vector between markets [

A final approach is to use ARCH-GARCH framework to analyze the transmission of volatility between markets. Dungey and Martin [

Focusing mainly on BRIC’s stock markets (Brazil, Russia, India, China), Aloui

A related work on contagion attempts to explain the transmission of volatility among stock markets, generally known as the volatility-spillover literature. Some studies on international spillovers concentrate on developed markets, especially the US, Japanese and major European markets (e.g., [

Other studies in this strand concentrate on emerging markets. Some focus on analyzing integration and interdependence in volatility across emerging markets, while others study the link between developing and developed markets.

Work related to this literature attempts to explain the transmission of shocks, and concentrates on financial crises and their effects on the evolution of financial spillovers and market behavior. Focusing on the Asian crisis, Gosh

For the recent financial crisis (2008–2009), Nikkinen

In this paper, we focus on studying the effect of the Global Financial Crisis on the intraday volatility transmission of three European markets (France, Germany, and the UK). The methodology of the study proceeds as follows. First, we identify the date of shock using the structured break test of Bai and Perron. Second, we apply the Flexible Fourier Form (FFF) procedure in order to use our high frequency 5 min intraday data and to deal with the problem of seasonality observed in intraday data. Then, after splitting our data into two periods according to the date of shock—pre-turmoil and turmoil—we study European markets returns by employing the bivariate vector autoregressive framework (VAR). According to this model, the returns of a given market are related to past returns of the same market and to the cross-market current and past returns in another market. Finally, we investigate the intraday volatility transmission by using an EGARCH model which captures the asymmetric impact of shocks on volatility.

This paper contributes to the existing literature on three fronts. First, papers such as [

The structure of the paper is organized as follows.

For empirical analysis, we use two different data sets. First, we use Standard & Poor’s 500 (S&P 500) daily index from 1 January 2004 to 31 December 2010 to identify the start date of the turmoil period, considered econometrically as the structural break in our data. S&P 500 price index was obtained from DataStream. Second, we use high frequency 5 min stock market price data of three stock markets, namely CAC40 (France), DAX30 (Germany), and FTSE100 (UK) from 1 July 2008 to 28 November 2008. Inspired by the event study methodology, and following the methodology used by many researchers (e.g., [

To split our data into two periods (calm and turmoil periods), we need, as a first step, to specify the crisis phase. Many researchers determine the date of beginning of the crisis based on major economic and financial events [

BP involves regressing the variable of interest on a constant and then testing for breaks within that constant. Therefore, it tests the null hypothesis—of no structural break—against a certain number of breaks. In our case, Bai and Perron may be presented as follows:
_{t} is the stock market price index at time t, θ_{k} is the mean of the price in the k^{th} regime, m represents the length of the time series, and ε_{t} represents the error term. BP requires two parameters for its implementation. First, it requires the minimum number of observations between breaks and second, it requires maximum number of possible breaks.

According to our results, the date of Structural break is on Friday, 12 September 2008 with 95% confidence intervals

The evolution of European stock markets indices (1 July 2008 to 28 November 2008).

_{t,n} | as a measure of volatility. The figure shows clearly the strong structure of the volatility. The intra-daily volatility shows the U-shape identified for most of the markets, and suggested by the model of Admati and Pfleiderer [

Average intraday volatility evolution in stock markets indices (1 July 2008 to 28 November 2008).

Note: The graph shows the average at intervals of five minutes of Absolute Returns |_{t}

Average intraday volatility before and during the turmoil period.

Before studying the spillover dynamics of stock markets indices returns we should, first, deseasonlize and standardize our high frequency 5 minute intraday data, in order to eliminate outliers and other anomalies present in such data. Second, we apply a bivariate VAR-EGARCH model to investigate the volatility and market behavior of the three European markets.

Descriptive statistics of data.

Whole Period |
Calm Period |
Turmoil Period |
|||||||
---|---|---|---|---|---|---|---|---|---|

RSCAC | RSDAX | RSFTS | RSCAC | RSDAX | RSFTS | RSCAC | RSDAX | RSFTS | |

Mean | −0.002332 | −0.001905 | −0.001426 | 0.000530 | 0.001422 | 0.000463 | −0.005036 | −0.005047 | −0.003211 |

Median | −0.003149 | −0.003858 | −0.004682 | −0.002501 | 0.000450 | −0.002814 | −0.004013 | −0.009451 | −0.008791 |

Maximum | 2.768749 | 2.838545 | 2.900669 | 1.132326 | 1.395331 | 1.060863 | 2.768749 | 2.838545 | 2.900669 |

Minimum | −1.673299 | −1.791665 | −3.044328 | −1.090163 | −1.079340 | −0.842513 | −1.673299 | −1.791665 | −3.044328 |

Std. Dev. | 0.232476 | 0.243903 | 0.226617 | 0.182200 | 0.185796 | 0.178694 | 0.271532 | 0.288201 | 0.264012 |

Skewness | 0.103355 | 0.107824 | 0.093690 | 0.071269 | 0.050567 | −0.034998 | 0.122225 | 0.133416 | 0.136466 |

Kurtosis | 6.938096 | 7.023621 | 12.08220 | 4.948796 | 5.879413 | 4.397209 | 6.305681 | 6.051845 | 11.88740 |

Jarque-Bera | 6939.780 | 7245.328 | 36825.20 | 827.5778 | 1799.296 | 424.2000 | 2521.581 | 2153.848 | 18144.36 |

Probability | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |

Observations | 10,710 | 10,710 | 10,710 | 5,202 | 5,202 | 5,202 | 5,508 | 5,508 | 5,508 |

This table shows the mean, the median, the maximum, the minimum, and the standard deviation (Std. Dev.) of stock indices returns. Note that these data are presented in a percentage format. The table also shows the skewness, the kurtosis coefficients and the normality test-Jarque-Bera test-of the three European Markets returns indices: the CAC40 (RSCAC), the DAX30 (RSDAX) and the FTSE (RSFTS). The data are provided for the whole period, the calm and the turmoil period.

We clean the high frequency stock price data for outliers and other anomalies before converting them into continuously compounded returns [_{t}_{t}_{t,n}_{t,n}_{t}

The deseasonalized and standardized intraday returns were then obtained respectively by:

We consider the EGARCH framework introduced by Nelson [

We use a bivariate VAR-EGARCH model to investigate the volatility of our series of returns of the CAC40, the DAX30 and FTSE100 indices.

The VAR(k)-EGARCH (1,1) model is given in the following way:

Equation (7) is a vector autoregressive (VAR) model of the conditional mean equation of returns on stock market index i (R_{i,t}). It means that R_{i} depends on previous own values of stock returns i (R_{i}), the cross-market current and past returns (R_{j}) and the random variable (ε_{i}). The random variable is conditionally Gaussian,
_{t − 1} the information set containing intradaily price information through period _{t}_{t}= ε_{t}/√h_{t} is the standardized innovation and E(|Z_{t}|) =

The second equation of the model (Equation (8)) represents the conditional variance of the stock market index returns. This equation means that the exponential conditional variance depends on the lagged value of innovation of the stock returns, the terms to capture asymmetric effects, and lag of conditional variance of the stock market return index. The parameters α_{i,j} with i = j captures the effect of the magnitude of a lagged innovation on the conditional variance, and when i ≠ j the coefficient captures the size and sign effect of a shock to market j on market i. Further,

The periodic character of the behaviour of the volatility inside the day of exchange is clearly illustrated via the correlative structure of autocorrelation of absolute returns [

The origin of this stylised feature was the intraday seasonality shown in

Once problems of outliers and periodicity have been addressed using FFF estimates, we can use our filtered and corrected data to investigate return and volatility spillover using the bivariate VAR-EGARCH estimates.

Autocorrelation of intraday absolute and deseasonalized index returns.

Note: The maximum lag length shown on horizontal axis is 10 days. The solid line represents the autocorrelations coefficients for absolute returns and the dotted line the autocorrelations coefficients for absolute deseasonalized returns.

We proceed with the estimation of the bivariate VAR-EGARCH model among the pairs of indices of: CAC40/DAX30, the CAC40/FTSE100 and the DAX30/FTSE100. Estimation results are reported in

For all pairs of indices, we note that, in most cases, the parameters of the model are statistically significant. These results provide evidence of return and volatility spillover among these markets. Note, however, that the levels of transmission of returns and volatility depend on both the pairs of markets and the period of study considered. Moreover, the estimated γ coefficients for the asymmetry effect are significant at the 5% level, which indicate the existence of an asymmetric response of volatility to shocks and justifies the use of EGARCH model. In the following sections, we analyse the return and volatility transmission according to each period in order to investigate the interrelationship among these European markets surrounding the break date.

The VAR terms (β_{i,j}) are estimated from the conditional mean equation of returns Equation (8). According to _{1,2} and β_{2,1} coefficients indicating respectively the return transmission from market 2 to market 1 and from market 1 to market 2 are statistically significant. This result shows that there is a significant return spillover between the markets, a finding in line with previous research (e.g., [

Moreover, the results indicate a more significant return spillover from DAX30 to both the CAC 40 and FTSE100, rather than the opposite. For example, considering the pair of indices DAX30/FTSE100, the parameter β_{1,2} is not significant, whereas the parameter β_{21} is significant and equal to 0.1516, suggesting that roughly 15.16% of the German returns innovation is transferred to the UK stock market.

VAR (1) EGARCH (1,1) CAC 40 FTSE 100 estimates.

β_{1,0} |
0.0001 | 0.0013 | 0.0594 | −0.0068 ** | 0.0031 | −2.2115 |

β_{1,1} |
−0.0980 *** | 0.0203 | −4.8173 | −0.1269 *** | 0.019 | −6.6757 |

β_{1,2} |
0.1253 *** | 0.023 | 5.4433 | 0.1255 *** | 0.0184 | 6.8089 |

β_{2,0} |
0.0003 | 0.0018 | 0.1959 | −0.0053 * | 0.0029 | −1.8372 |

β_{2,1} |
0.0409 ** | 0.02 | 2.0482 | 0.0340 * | 0.0187 | 1.8172 |

β_{2,2} |
−0.0081 | 0.0223 | −0.3648 | 0.0118 | 0.017 | 0.6939 |

α_{1,0} |
−0.6520 *** | 0.0788 | −8.2732 | −0.1839 *** | 0.0306 | −6.017 |

α_{1,1} |
0.0732 *** | 0.0207 | 3.5432 | 0.1598 *** | 0.0191 | 8.3607 |

α_{1,2} |
0.1141 *** | 0.0213 | 5.3674 | 0.0845 *** | 0.0149 | 5.6717 |

α_{2,0} |
−0.5698 *** | 0.0062 | −91.7875 | −0.1912 *** | 0.0299 | −6.4019 |

α_{2,1} |
0.0558 *** | 0.0171 | 3.2598 | 0.2253 *** | 0.0196 | 11.4981 |

α_{2,2} |
0.1050 *** | 0.0203 | 5.1841 | 0.0460 *** | 0.0146 | 3.1477 |

γ_{12} |
0.5602 * | 0.3016 | 1.8571 | −0.0938 *** | 0.033 | −2.8477 |

γ_{21} |
−0.4119 ** | 0.1643 | −2.5075 | −0.2250 *** | 0.0828 | −2.7162 |

δ_{1} |
0.8087 *** | 0.0229 | 35.2466 | 0.9287 *** | 0.0115 | 80.783 |

δ_{2} |
0.8344 *** | 0.0024 | 353.2126 | 0.9278 *** | 0.011 | 84.6729 |

ρ | 0.8060 *** | 0.0046 | 174.3189 | 0.8329 *** | 0.0036 | 232.3012 |

Q_{CAC}(20) |
27.60 | 24.612 | ||||

Q_{FTSE}(20) |
29.155 | 26.054 | ||||

Q²_{CAC}(20) |
25.661 | 21.739 | ||||

Q²_{FTSE}(20) |
21.525 | 21.441 |

Note: Data are obtained using 5 min deseasonalized and standardized returns. β_{i,j} are coefficients of the regression of the VAR equation—conditional mean equation of returns (Equation (7)). The specification and optimal lags of the VAR equation are chosen according to likelihood ratio tests and Akaike (AIC) and Schwarz (SIC) information criteria, respectively. The coefficients α, γ and δ are coefficients of the regression of the conditional variance of returns (Equation (8)). The asymmetric terms γ are statistically significant witch confirms the use of EGARCH model. The Q-test of correlation Q(20) and Q²(20) does not reject the null hypothesis of no serial correlation (using 20 lags). CAC40 refers to market 1 and FTSE100 to market 2. *, **, *** represent statistical significance at 10%, 5% and 1% respectively.

VAR (1) EGARCH (1,1) DAX 30 FTSE 100 estimates.

β_{1,0} |
0.0009 | 0.0025 | 0.3609 | −0.0051 * | 0.0031 | −1.667 |

β_{1,1} |
0.0166 | 0.0209 | 0.7939 | −0.0639 *** | 0.0163 | −3.9165 |

β_{1,2} |
0.0011 | 0.0212 | 0.0508 | 0.0318 ** | 0.0161 | 1.9744 |

β_{2,0} |
0.0006 | 0.0024 | 0.2618 | −0.0035 | 0.003 | −1.1677 |

β_{2,1} |
0.1516 *** | 0.0197 | 7.6869 | 0.0941 *** | 0.0164 | 5.734 |

β_{2,2} |
−0.0915 *** | 0.0206 | −4.4342 | −0.0411 ** | 0.0174 | −2.3638 |

α_{1,0} |
−0.5183 *** | 0.0963 | −5.3824 | −0.0869 *** | 0.0141 | −6.1684 |

α_{1,1} |
0.1373 *** | 0.0208 | 6.5894 | 0.1705 *** | 0.0147 | 11.6273 |

α_{1,2} |
0.0323 | 0.0205 | 1.5715 | 0.0165 | 0.0117 | 1.4082 |

α_{2,0} |
−0.4229 *** | 0.0792 | −5.3407 | −0.1270 *** | 0.0209 | −6.0909 |

α_{2,1} |
0.0758 *** | 0.0182 | 4.152 | 0.1795 *** | 0.0161 | 11.1249 |

α_{2,2} |
0.0859 *** | 0.0209 | 4.109 | 0.0681 *** | 0.0123 | 5.53 |

γ_{12} |
−0.049 | 0.0754 | −0.6501 | −0.1301 *** | 0.0393 | −3.3083 |

γ_{21} |
−0.1007 | 0.0931 | −1.0824 | −0.0314 * | 0.1092 | −1.9881 |

δ_{1} |
0.8452 *** | 0.0285 | 29.6699 | 0.9639 *** | 0.0055 | 174.1163 |

δ_{2} |
0.8770 *** | 0.0228 | 38.4051 | 0.9508 *** | 0.0077 | 122.8481 |

Ρ | 0.7521 *** | 0.0059 | 127.4695 | 0.7783 *** | 0.0051 | 151.5845 |

Q_{DAX}(20) |
29.602 | 23.048 | ||||

Q_{FTSE}(20) |
27.648 | 20.226 | ||||

Q²_{DAX}(20) |
18.812 | 12.377 | ||||

Q²_{FTSE}(20) |
17.303 | 19.255 |

Note: Data are obtained using 5 min deseasonalized and standardized returns. β_{i,j} are coefficients of the regression of the VAR equation—conditional mean equation of returns (Equation (7)). The specification and optimal lags of the VAR equation are chosen according to likelihood ratio tests and Akaike (AIC) and Schwarz (SIC) information criteria, respectively. The coefficients α, γ and δ are coefficients of the regression of the conditional variance of returns (Equation (8)). The asymmetric terms γ are statistically significant witch confirms the use of EGARCH model. The Q-test of correlation Q(20) and Q²(20) does not reject the null hypothesis of no serial correlation (using 20 lags). CAC40 refers to market 1 and FTSE100 to market 2. *, **, *** represent statistical significance at 10%, 5% and 1% respectively.

VAR (2) EGARCH (1,1) CAC 40 DAX 30 estimates.

β_{1,0} |
−0.0003 | 0.0022 | −0.1555 | −0.0045 * | 0.0025 | −1.8015 |

β_{1,1} |
−0.2742 *** | 0.0248 | −11.0468 | −0.1438 *** | 0.0189 | −7.5974 |

β_{1,2} |
−0.0810 *** | 0.0245 | −3.3041 | 0.1649 *** | 0.0171 | 9.655 |

β_{1,3} |
0.3156 *** | 0.0231 | 13.6933 | |||

β_{1,4} |
0.0475 * | 0.025 | 1.904 | |||

β_{2,0} |
0.0003 | 0.0023 | 0.1407 | −0.0050 * | 0.0026 | −1.8952 |

β_{2,1} |
−0.0375 | 0.0251 | −1.4949 | 0.0442 ** | 0.0184 | 2.4 |

β_{2,2} |
−0.0217 | 0.025 | −0.868 | −0.0767 *** | 0.0167 | −4.5822 |

β_{2,3} |
0.0441 * | 0.0228 | 1.93 | |||

α_{1,0} |
−0.5982 *** | 0.0898 | −6.6635 | −0.0251 *** | 0.0097 | −2.5853 |

α_{1,1} |
0.0373 * | 0.0224 | 1.661 | 0.0047 *** | 0.0007 | 7.1456 |

α_{1,2} |
0.1748 *** | 0.0249 | 7.014 | 0.1107 *** | 0.0094 | 11.7436 |

α_{2,0} |
−0.6357 *** | 0.1367 | −4.6502 | −0.0204 ** | 0.009 | −2.2539 |

α_{2,1} |
0.0044 | 0.023 | 0.1928 | 0.0046 *** | 0.0007 | 6.954 |

α_{2,2} |
0.1951 *** | 0.0272 | 7.1742 | 0.1141 *** | 0.0082 | 13.9236 |

γ_{12} |
0.1976 | 0.2764 | 0.715 | −11.135 *** | 0.0785 | −141.822 |

γ_{21} |
−0.0893 * | 0.0504 | −1.7731 | 0.2671 *** | 0.0486 | 5.5001 |

δ_{1} |
0.8249 *** | 0.026 | 31.7162 | 0.9894 *** | 0.0036 | 276.041 |

δ_{2} |
0.8099 *** | 0.0404 | 20.0285 | 0.9908 *** | 0.0034 | 287.5268 |

ρ | 0.8341 *** | 0.0038 | 221.2988 | 0.8283 *** | 0.0044 | 188.0018 |

Q_{CAC}(20) |
27.665 | p-value 0.073 | 25.433 | p-value 0.209 | ||

Q_{DAX}(20) |
29.377 | p-value 0.059 | 23.058 | p-value 0.310 | ||

Q²_{CAC}(20) |
32.485 | p-value 0.052 | 21.739 | p-value 0.363 | ||

Q²_{DAX}(20) |
25.211 | p-value 0.197 | 26.162 | p-value 0.215 |

Note: Data are obtained using 5 min deseasonalized and standardized returns. β_{i,j} are coefficients of the regression of the VAR equation—conditional mean equation of returns (Equation (7)). The specification and optimal lags of the VAR equation are chosen according to likelihood ratio tests and Akaike (AIC) and Schwarz (SIC) information criteria, respectively. The coefficients α, γ and δ are coefficients of the regression of the conditional variance of returns (Equation (8)). The asymmetric terms γ are statistically significant witch confirms the use of EGARCH model. The Q-test of correlation Q(20) and Q²(20) does not reject the null hypothesis of no serial correlation (using 20 lags). CAC40 refers to market 1 and FTSE100 to market 2. *, **, *** represent statistical significance at 10%, 5% and 1% respectively

As regards the intraday volatility spillover (Equation (9)), the estimated α _{1,2} and α _{2,1} coefficients indicate respectively the volatility transmission from market 2 to market 1 and from market 1 to market 2. For example, considering the pair of indices CAC40/FTSE100 (

Turning to the turmoil period the analysis reveals, first, that the coefficients of asymmetry (γ_{i,j}) are significant during this period. This result is not surprising, as during the turbulent period good news may have a bigger impact than negative news, unlike what happens during calm periods. The (δ_{i}) coefficients, which measure the impact of all past shocks on the current conditional variance, are also highly significant and approach one during the turbulent period. This result is expected as the markets are in a continuous process of turbulence and the clustering phenomenon is observed.

Second, the estimated coefficients indicating the return (β_{1,2} and β_{2,1}) and the volatility (α _{1,2} and α _{2,1}) transmission are mostly statistically significant. These results can confirm the strong interrelationship among markets during turmoil period.

Third, we observe that the German market continues to influence returns and volatility of British and French markets. Hence, up to 9.41% and to 16.49% of respectively the returns of FTSE100 and CAC40 indices are explained by German market. Considering the volatility behavior, around 17.95% of British market volatility is affected by German market. The impact is relatively less important on French market, where the volatility spillover coefficient α _{1,2} is equal to 11.07%.

Focusing on the level of correlation of returns (ρ) between the markets, it increased after the break date—except for the French-German pair, where the correlation remains relatively constant; the coefficient between German and UK indices rose from 0.75 to 0.78, and from 0.8 to 0.83 for the French and UK indices. These results confirm those of Forbes and Rigobon [

A comparative analysis between calm and turmoil periods shows that, with regards to return spillover, the magnitude of transmission is roughly the same between the two periods. However, in term of volatility spillover, the transmission was more important during turmoil periods. Our findings do not offer evidence of contagion induced by the crisis. The increase of volatility after the structural break seems to be induced mainly by the interdependence of markets due to normal linkages between them. These results also confirm previous studies showing that European markets were deeply affected by US market and shocks emanating from it, which had led to the Global Financial Crisis, e.g., [

This article studies stock market volatility behavior of three European markets,

The analysis of correlation coefficients shows that the three indices—the DAX 30, CAC 40, and FTSE 100—are highly intercorrelated, and that these correlations become slightly more important during the turbulent period. These results support a general pattern of coupling for the three markets during the whole period of study, with an increase in the coupling during the turmoil phase. This argument is further supported by the findings of Dimitriou

Focusing on return and volatility behavior stock markets, we also found that German market influences French and UK markets, especially during turmoil period. Germany seems to have been seen as the hub of financial and economic activity in Europe during the period of study. These findings raise question concerning the role of market consensus

Our findings have implications for international investors. Evidence on deep interdependence between European markets calls into question the advantages of investing in multiple European markets in order to diversify a portfolio, especially during turmoil periods. On the other hand, since European markets seem to be widely influenced by German market, special attention should be given by those who invest in Europe to the economic, financial, and political prospects of Germany.

The results also provide implications for European policy makers about the decisions and directions to take to better protect markets from contagion and financial collapse. They should examine the possible strategies to reduce the inter-relationships between markets, and especially to mitigate, as far as possible, German influence. These findings can also be relevant to Asian policy makers debating the advantages and disadvantages of increasing financial integration in the region.

In such a financial context—becoming more and more integrated—there is a great interest in identifying potential gains from international portfolio diversification. This should lead to the development of more in-depth studies focusing on stock market relationships. Future research could better explain the role of investor behavior in interdependence of financial markets and impact of the crisis.

The authors would like to thank the anonymous referees for their helpful comments that contributed to improve the final version of the paper. They would also like to thank the editor for his support during the review process. Finally, they would like to thank the participants of the 2nd International Symposium in Computational Economics and Finance (Tunis) and the 19th Annual Conference of the Multinational Finance Society (Krakow). We are also grateful to Nanci Healy for language editing.

The authors declare no conflict of interest.

We calculate returns using the equation Ri,t = 100 × (lnPi,t – lnPi,t-1) where Ri,t is the return for stock market index i at time t, ln(Pi,t) is the log of stock price at time t, and ln(Pi,t-1) is the log of the laged value of the stock price at time t. Following Andersen

We assume that: E(Rt,n) = 0, E(Rt,n , Rs,m) = 0 and that the variance and covariance of squared returns exist and are finite. The continuously compounded daily squared returns may be decomposed as: Rt ² = (∑Rt,n²).

Following Andersen

We use VAR(1)-EGARCH (1,1) for the three bivariate relations during calm and turbulent periods except for the CAC40/DAX30 pair during the calm phase where a VAR(2)-EGARCH(1,1) is more appropriate.