TERRENO

The sample includes daily returns of nine European sovereign bond indices, from 2 Jan 2001 to 22 May 2014. In order to estimate the changes of dependence structure,

the whole sample period is decomposed into two sub-periods20. One period takes

the tranquil market conditions in account, the other one is relatively turmoil period.

The decomposition of the sample period is based on with three reasons. First,

Dajcman (2012) denotes that the time for the occurrence of the Greek Debt Crisis

is 23 April 2010, which is the time the Greek government requested a bailout from the institution of EU/IMF. Second, Adel and Salma (2012) claims a tranquil period that is characterized by calm volatility, and a turmoil period that is characterized by frantic volatility (The relevant evidence can be partially summarized from fig.1.10). Finally, the evidence summarized from fig.1.11 shows that for most of countries, the occurrence of contagion happened at least four months prior to the time the Greek government requested a bailout from EU/IMF. In summary, we determine the bound date between ”a tranquil period” and ”a crisis period” in the light of all above evidences. The bound date should be earlier than the dates summarized from above evidence, so that the post-crisis period will include all turmoil information of the European debt crisis. Therefore, the bound date is decided to be 1 Sep 2009. Thus, the pre-crisis period of European sovereign debt crisis is from 2 Jan 2001 to 1 Sep 2009, and the post-crisis period is from 2 Sep 2009 to 22 May 2014.

In the approach of copula-GARCH, we consider the marginal method presented in section 1.2.1, and the traditional GARCH model and GJR model following normal and student-t distributions to add the asymmetry information. Specifically, we use the univariate GARCH model to derive the univariate marginal model. Allowing the univariate GARCH model helps produce the probability distributions and the results of maximum likelihood (See table 1.4 and 1.5). In table 1.4 and 1.5, parameters of

20_{Following two-period approach ofAdel and Salma (2012) will help observe the changes of the}

the GARCH-normal, GARCH-t, GJR-normal and GJR-t are respectively estimated and reported. As a result, all parameters for two-period are statistically significant

and non-zero, which therefore are sufficient for the copula estimation. We also

present the results for the AIC (Akaike information criterion) and BIC (Bayesian information criterion). The results show all estimated AIC and BIC lying between -11 and -8.

Three copulas are applied in our estimation, they are Gaussian, Student-t and Clayton, respectively. We continue to test the parameters of three chosen copulas, the results are shown in table 1.6 and 1.7. We use Inference function for margins

(IFM) method as a default copula estimation method. Following Rodriguez (2007),

Kendall’s tau is used to estimate the parameters of Student-t Copula, is defined as:

ρτ

2

πarcsinpρq (1.29)

.

Table 1.6 reports the estimations for the dependence parameters of three copulas and model fitness, during the period of 2 Jan 2001 to 1 Sep 2009. And table 1.7 reports those during the period of 2 Sep 2009 to 22 May 2014. We first focus on the copula fit for the pre-crisis sample. For GARCH models, with the relatively smaller values of AIC and BIC, Gaussian and Student-t seem to be better fitting copulas overall. For GJR models, Gaussian and Student-t copulas are overall better fitting copulas as well. And then, during the the period of 2 Sep 2009 to 22 May 2014 (post-crisis sample), we find the mixed results for the copula fitness. Although there are big differences among AIC and BIC of different countries, they are still acceptable.

From table 1.6 and 1.7, all parameters for dependence between Greece and each of eight European countries are positive and strongly significant. We surprisingly find a significant increase for all dependence parameters of copulas from the table 1.6 and

1.7. The high level of nonlinear dependence somewhat reflects the strongly nonlinear contagion and indicates that all European sovereign bond markets are highly exposed to the Greek bond market. The nonlinear results of copula GARCH model support the conclusions obtained by cross-country DCC-GARCH approach. After adding the asymmetry information by using GJR-normal model, the parameters of Student-t copula sharply increases from 0.004 to 0.1380 on average (the most growth). This growth is significantly larger than the increase of the other dependence parameters. Hence, we consider that the asymmetry information of GJR-normal model will be

robust in improving the explanatory power of Student-t copula. The Student-t

copula becomes more sensitive to detecting changes in the dependence structure. Relating this result to Rodriguez (2007), they put forward that Student-t copula is often used on the symmetric tail dependence and tail independence. Nonetheless, we find that Student-t copula will be more powerful to detect the changes of tail dependence, with the asymmetry counterpart of GJR-normal model.

All in all, sovereign bond contagion has been found by the two-period analysis of dependence parameters. Furthermore, different types of GARCH-type models, especially in GJR-normal model, may increase or decrease the copula’s ability of estimating the changes of the extreme tail dependence.

1.3.4

Contagion analysis within European region: Multino-