Financial contagion is the cross-market transmission of shocks or the general cross-market spillover effects. It can take place both during "good" times and "bad" times. Then, contagion does not need to be related to crises. However, it is emphasized during crisis times.
Understanding and describing contagion are essential for coping with financial crises. In fact, the presence of financial contagion among markets can mitigate the effects of diversification of investments precisely when they are needed most. In our study we follow the so called "spatial" approach introduced by Bradley and Taqqu in 2004. Roughly speaking, there is contagion from market X to market Y if there is more dependence between X and Y when X is doing badly than when X exhibits typical performance, that is, if there is more dependence at the loss distribution of X than at its center. One of the main features of this approach is that it ``does not require any definition of crisis and normal periods and it is not temporal in nature''.

We propose the following definition of contagion (Durante, Jaworski 2009). Let X and Y be the random variables representing returns of two financial markets. Thus, contagion is defined as an increase of the dependence in some tail regions of the joint distribution of (X,Y) with respect to some central regions. Moreover, as just copulas describe the dependence among random variables, contagion refers to the comparison among threshold copulas obtained with respect to tail regions or central regions of the unit square.

As an empirical illustration of the above methodology we consider two markets:
the New York Stock Exchange (US) and SWX Swiss Exchange AG in Zurich (Switzerland). We compare the daily log-returns of the indices - Dow Jones Industrial Average (DJIA) and Swiss Market Index (SMI) related to the period November 1990 - March 2009.

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3. On tail expansions of copulas and modeling multivariate extremes.