This paper focuses on measuring risk due to extreme events going beyond the multivariate normal distribution of joint returns. The concept of tail dependence has been found useful as a tool to describe dependence between extreme data in finance. Specifically, we adopted a multivariate Copula-EGARCH approach in order to investigate the presence of conditional dependence between international financial markets. In addition, we proposed a mixed Clayton-Gumbel copula with estimators for measuring both, the upper and lower tail dependence. The results showed significant dependence for Singapore and Malaysia as well as for Singapore and US, while the dependence for Malaysia and US was relatively weak