This paper is related to some recurrent concerns in the economic and financial literatures. In the former one, it is linked to the notion of contagion between international markets, and in particular the propagation of financial crises between neighbouring countries and their repercussion on economic activity. Such concern has recently gained increased interest in view of the emerging markets crises in the nineties. In the latter one, it is linked to the notions of risk and portfolio diversification. In recent years, risk management methods such as VaR or the enlargement of financial integration to a broader scope of countries have renewed the interest in these topics.
Both literatures meet in their requirement to model the dependence between financial markets. With very few exceptions, the empirical treatment of this problem rests on standard statistical tools and/or standard econometric methods (regression methods, time series method, dichotomous models, quantile regressions). A commonly used tool is the standard (Pearson) correlation coefficient. One of the purpose of this paper is to argue that the use of this tool can lead to very misleading inference in this context. A well-known reason (see e.g. Boyer, Gibson, Loretan [1999] or Forbes and Rigobon [1999]) is that it is not robust to heteroskedascity (i.e. the fact that volatility is time-varying). As we shall below, other reasons can be invoked to be doubtful about analysis based on the Pearson correlation coefficient.
Recently, Straetmans [1999], St?aric?a [1999] and Longin and Solnik [2000] have proposed to rely on extreme value theory (EVT), and especially on multivariate tools associated with this literature, to analyse dependence between financial markets. As an extension, this paper relies on the notion of copulas which generalizes their approach and is rather new in this context (see however Embrechts, McNeil and Straumann [1999] or Bouyé, Durrleman, Nikeghbali, Riboulet and Roncalli [2000]). In broad terms, a copula can be defined as the dependence function between random variables. More precisely, it can be seen as a function that links univariate marginals to their full multivariate distribution.
While they were introduced in 1959, the literature on copulas, and especially the study of their statistical properties and their applications, only developed in recent years. The main purpose of this paper is to introduce a conceptual framework based on copulas for the analysis of the dependence between financial markets. Furthermore, we propose two applications.The first ones concerns the study of extreme dependence between international equity markets. The second one concerns the analysis of the East-Asian crisis.
The layout of the paper is as follows. Section 2 operates a literature review on the dependence between financial markets with special emphasis on empirical methods. Section 3 offers introductions to copulas and multivariate extreme value theory and propose a new statistical framework based on copulas. Furthermore, it presents illustration of the associated tools with an application to the interactions between three major stock indexes (CAC 40, Dow Jones and Nikkei). Section 4 presents the application to the analysis of the Asian crisis. Section 5 concludes the article.
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Revisiting the dependence between financial markets with copulas
