مقاله سال ۲۰۱۶

The dependence structure of financial markets is a key and debatable issue for financial economists, regulators and investors. It is the useful and important information for some financial activities, such as international portfolio’s diversification and risk management, derivative pricing, and market integration (Buccheri, Marmi, & Mantegna, 2013). For example, how to select financial assets in the international portfolio diversification is the crucial step, which needs to examine the dependence of financial asset returns and check whether they have the dependence hierarchical or clustering structure. As such, a growing number of methods are developed to capture the dependence structure among different financial asset returns, while the dependence (or correlation) network analytical tool is one of the most popular and widely used approaches (see, e.g.,Brida, Gómez, & Risso, 2009; Brida & Risso, 2010; Fenn et al., 2012; Kwapien & Dro ´ zd˙ z, 2012; Kwapie ˙ n, Gworek, & Dro ´ zd˙ z, 2009; Man- ˙ tegna, 1999; Tumminello, Lillo, & Mantegna, 2010; Wang, Xie, Chen, & Chen, 2013a; Wang, Xie, Han, & Sun, 2012). Different approaches can be used to build the dependence network, such as the minimum spanning tree (MST) approach (Mantegna, 1999), the planar maximally filtered graph (PMFG) method (Tumminello, Aste, Matteo, & Mantegna, 2005), and the correlation threshold method (Boginski, Butenko, & Pardalos, 2005; Onnela, Kaski, & Kertész, 2004), which are designed to select or filter the information presented in the dependence (or correlation) matrix. In other words, before constructing the financial networks, one should build the dependence matrix of the financial asset returns by the dependence measure, while the common practice of the dependence measure is chosen as the Pearson’s correlation coefficient (PCC). Although PCC is easy to calculate and widely used, some questions are posed on the practice of using PCC as a universal dependence measure (see, e.g., Rachev, Fabozzi, & Menn, 2005; Wang et al., 2012; Zebende, 2011; Zhou & Gao, 2012).

There are at least two drawbacks for PCC as follows. (1) The theoretical assumption of PCC is that the joint distributions of time series obey Gaussian distribution. However, a large deal of evidence shows that the dependence between different financial asset returns is nonGaussian (see, e.g., Bae, 2003; Durante, Foscolo, Jaworski, & Wang, 2014; Wang, Xie, Zhang, Han, & Chen, 2014). A good instance is that the dependence of financial asset returns during a recession is larger than during a boom (Zhou & Gao, 2012). Besides, many studies report that the dependence of financial markets comes to a remarkable peak during the largest market shocks and financial crises (see, e.g., Aste, Shaw, & Di Matteo, 2010; Podobnik, Wang, Horvatic, Grosse, & Stanley, 2010; Wang, Xie, Chen, Yang, & Yang, 2013b). (2) PCC is defined to quantify the linear correlation for the whole range of sample. It ignores the fact that the real world data are characterized by a high level of heterogeneity (Wang et al., 2013b). Namely, it neglects the difference between extreme and commonplace observations. It is a fact that as the frequency of financial crisis doubled in recent years, the extreme returns of financial time series occurred increasingly. Therefore, PCC may lose effectiveness and be misleading if the investigated asset returns are heterogeneous and the extreme returns show different patterns of dependence from the remaining returns (Zhou & Gao, 2012). In a word, the previous dependence network methods cannot accurately detect the dependence structure of financial markets, especially during the financial crises (e.g., US sub-prime crisis, 2008 fi- nancial crisis, and European debt crisis).

To overcome the shortcomings of linear correlation functions (e.g., PCC), scholars resort to a powerfully and widely used tool—copulas proposed by Sklar’s (1959). Copulas are flexible and effective tools to measure dependence structure between two or more variables and model any type of multivariate distributions, which go beyond the linear correlation. Specifically, they allow for the tail dependence that represents the level of dependence among the tails of financial asset distributions (Sun, 2013; Zhou & Gao, 2012). In detail, tail dependence refers to the level of dependence in the lower and upper quadrant tails of a bivariate distribution, so it is a suitable measure of the dependence of extreme events. That is to say, tail dependence can be divided into two measures, namely the lower-tail dependence and upper-tail dependence, which are used respectively to investigate the joint extreme events in financial asset returns during the market downturns and market upturns (Hu, 2010). However, in the common practice of measuring dependence, people usually ignore the extreme returns that hide in the tails and the tail dependence among financial asset returns, which is dangerous for investment portfolios and other financial activities especially during the market downturns. So, more attentions should be paid to the tail dependence of financial markets. Unfortunately, to the best of our knowledge, very little of the existing research considers the tail dependence of the foreign exchange (FX) market from a network point of view.