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This paper studies the relatedness and the model construction of exchange rate volatility and the South Korea stock market returns. Empirical results show that we can construct a bivariate EGARCH(1, 2) model with a dynamic conditional correlation (DCC) to analyze the relationship of exchange rate volatility and Korea stock market returns. The average estimation value of the DCC coefficient for these two markets equals to -0.1961, this result indicates that the exchange rate volatility negatively affects the South Korea stock market. Empirical result also shows that there exists an asymmetrical effect on the South Korea stock market, but the exchange rate volatility does not have the asymmetrical effect. Based on the good news and bad news (Nelson, 1991) of the stock market, the bivariate EGARCH(1, 2) model with a DCC has the better explanation ability compared to the bivariate GARCH(1, 1) model.