The main purpose of this study is to analyse comparatively the characteristics of volatility between yen-dollar and won-dollar exchange rate since the global financial crisis of 2008. Therefore, this study focuses on analysing the market persistency effect, the asymmetry effect and the conditional heteroscedasticity by using GARCH, GJR, and Dummy-GARCH models. Some empirical results of this study are summarized as follows; Firstly, in terms of market persistency, the median lag of won-dollar exchange rate(1.55 day and 9.48 day) was larger than that of yen-dollar exchange rate(0.93 day and 5.52day) respectively in the first period (2008.9~2012.11) and in the second period(2012.12~2017.12). Specially, a market unefficiency effect was found in the second period. Secondary, contrary to the result of won-dollar, an evidence was found in detecting the asymmetry effect of volatility of yen-dollar exchange rate. Thirdly, the mutation of exchange rate volatility was found negatively in case of yen-dollar and won-dollar exchange rate in the second period. Therefore, this paper suggested the importance of the risk management of exchange rates under the circumstance of Japanese continuous quantitative easing(QE) in 2018.