In this paper, we study the correlation between exchange rates and stock markets for United States, Canada, and Mexico between 2005 and 2010, especially the period of the global financial crisis. For the dependence structure between a exchange rate and a stock market, a copula model is exploited due to the asymmetry dependence observed. Note that the asymmetric dependence leads to be significantly stronger as putting money into the long-term investment. In order to specify the exact correlation, the tail dependence and exceedance correlation are both employed. In our empirical analyses, the phenomenon of asymmetric dependence between exchange rates and stock markets all occur in United States, Canada, and Mexico after the global financial crisis, meaning that arbitrage exists.